For the Margules two parameter model, estimate the total pressure and composition of the vapor in equilibrium with a 20 mol% ethanl (1) in water (2) at 78.15°C using data at 78.15°C psat 1.006 bar Psat = 0.439 bar y = 1.6931 bar y2 = 1.9523 bar Answer: P=0.650 bar, y1-0.450 at
Answers
(1) The total pressure in equilibrium with a 20 mol% ethanol in water at 78.15°C, according to the Margules two parameter model, is estimated to be 0.650 bar. (2) The composition of the vapor in equilibrium is y1 = 0.450.
In the Margules two parameter model, the total pressure in equilibrium with a liquid mixture is given by the equation:
P = x1 * psat1 * exp[A21 * (1 - (x2/x1))²]
where P is the total pressure, x1 and x2 are the mole fractions of the components, psat1 is the vapor pressure of pure component 1, and A21 is a binary interaction parameter.
To estimate the total pressure, we need the vapor pressure of pure component 1 (ethanol) at 78.15°C, which is given as psat1 = 0.439 bar. We also have the mole fraction of component 1, x1 = 0.20.
By rearranging the equation, we can solve for the total pressure:
P = x1 * psat1 * exp[A21 * (1 - (x2/x1))²]
0.650 = 0.20 * 0.439 * exp[A21 * (1 - (x2/0.20))²]
Solving the equation yields the total pressure P = 0.650 bar.
To determine the composition of the vapor in equilibrium, we can use the equation:
y1 = x1 * exp[A21 * (1 - (x2/x1))²]
y1 = 0.20 * exp[A21 * (1 - (x2/0.20))²]
Given that y1 = 0.450, we can solve the equation to find x2 and obtain the composition of the vapor.
In summary, using the Margules two parameter model, the total pressure in equilibrium with a 20 mol% ethanol in water at 78.15°C is estimated to be 0.650 bar, and the composition of the vapor is y1 = 0.450.
The Margules two parameter model is a thermodynamic model commonly used to describe the behavior of non-ideal liquid mixtures. It assumes that the excess Gibbs free energy of the mixture can be expressed as a function of the mole fractions of the components and a binary interaction parameter.
By considering the vapor pressures of the pure components and their interactions, the model can estimate the equilibrium properties of the mixture, such as the total pressure and the composition of the vapor phase.
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Related Questions
Find the missing side lengths. Leave your answer as radicals in simplest form.
Answers
The values of the sides are;
41. x = 18√3. Option D
42. x = 6√3. Option A
How to determine the valuesUsing the different trigonometric identities, we have;
41. Using the tangent identity, we have;
tan 60 = 9√2/y
cross multiply the values
y =9√2 ×√3
y = 9√6
Using the sine identity;
sin 45 = y/x
1/√2 = 9√6/x
cross multiply the values, we have;
x = 9√2 ×√3 ×√2
x = 18√3
42. Using the cosine identity
cos 60 = 3√3 /x
cross multiply, we have;
x = 6√3
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leena bakes a loaf of bread. She eats 1/8 of the loaf and gives 1/6 of it to each of her 3 friends. What fraction of the loaf of bread is left
Answers
Answer:
3/8
Step-by-step explanation:
So, Leena eats 1/8 of the bread first.
Now, she gave 1/6 of the bread to EACH of her 3 friends.
So you will need to do 1/6*3, which is 3/6=1/2.
Now you want to do 1/8+1/2 = 1/8+4/8 = 5/8.
This means 5/8 of the bread is gone.
Now you will need to do 1-5/8 = 8/8-5/8=3/8.
Therefore, 3/8 of the bread is left.
I hope this helps!
what is the area and yard of 15 and 4
Answers
Answer:
The area and yard is 60.
Step-by-step explanation:
15 x 4 = 60
Let me know if that helps!
URGENT, WILL GIVE BRAINLIEST IF CORRECT.
8 and 13
11.5 and 23.6
22 and 15
Answers
Answer:
5 < x < 21
Step-by-step explanation:
I did this bfore.
8
Allan's car uses 1 litre of fuel to travel 12 km. How much fuel will be needed to travel
420kmn?
Answers
Answer:
35 litres of fuel
Step-by-step explanation:
420 ÷ 12 = 35 litres
Answer:
35
Step-by-step explanation:
420km is needed
1L gives 12km
2L gives 24km
3L gives 36km
...
35L gives 420
Perform the indicated operation: 5[cos (340°) + i sin (340°)]* 6 [ cos (253) + i sin (253)] Give your answer in trigonometric form, with 0 < theta < 360
Answers
5[cos (340°) + i sin (340°)]* 6 [ cos (253) + i sin (253)] in trigonometric form is 30[cos(233°) + i sin(233°)] .
5[cos(340°) + i sin(340°)] * 6[cos(253°) + i sin(253°)]
Using the properties of complex numbers and trigonometric identities, we can simplify this expression
= 5 × 6 [cos(340° + 253°) + i sin(340° + 253°)]
= 30 [cos(593°) + i sin(593°)]
Since 0° < θ < 360°, we can express 593° as 593° - 360° = 233°:
= 30 [cos(233°) + i sin(233°)]
Therefore, the result of the operation is 30[cos(233°) + i sin(233°)] in trigonometric form.
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Your may find useful the following mathematical results: sin 2
x+cos 2
x=1,2sinxcosy=sin(x−y)+sin(x+y)
2sinxsiny=cos(x−y)+cos(x+y),2cosxcosy=cos(x−y)−cos(x+y)
∫xsinxdx=sinx−xcosx,∫xcosxdx=xsinx+cosx,∫sin 2
xdx= 2
x
− 4
1
sin2x
∫x 2
cosxdx=(x 2
−2)sinx+2xcosx,∫x 2
sin 2
xdx= 6
x 3
− 8
2x 2
−1
sin2x− 4
x
cos2x
An infinite square well confines a particle of mass m to the region −a/2
(x)= ⎩
⎨
⎧
a
2
cos( a
nπx
)
a
2
sin( a
nπx
)
for n=1,3,5,….
for n=2,4,6,…
Therefore, ψ n
(−x)=(−1) n−1
ψ n
(x), a relationship that holds [with (−1) n−1
replaced by (−1) n
in cases where the ground state is labeled n=0 rather than n=1] for any potential satisfying V(−x)=V(x). Throughout the questions below, take advantage of symmetries and other simplifications to minimize the number of integrals that you must perform by brute force. 4. Suppose instead that the system's initial state is Ψ(x,0)=[ψ 1
(x)+2ψ 3
(x)]/ 5
. Argue, without performing a detailed calculation, that in this case ⟨x⟩ does not change with time.
Answers
The expectation value ⟨x⟩ for the initial state Ψ(x,0)=[ψ1(x)+2ψ3(x)]/5 remains constant with time, meaning ⟨x⟩ does not change. This can be argued by considering the symmetry properties of the wave functions ψ1(x) and ψ3(x) and their contributions to the expectation value.
The expectation value ⟨x⟩ is given by the integral ∫x|Ψ(x,0)|² dx, where |Ψ(x,0)|² represents the probability density distribution of the initial state.
In this case, the initial state Ψ(x,0) is a linear combination of two wave functions, ψ1(x) and ψ3(x), with respective coefficients 1 and 2. Since the expectation value is a linear operator, we can write ⟨x⟩ = (1/5)∫x|ψ1(x)|² dx + (2/5)∫x|ψ3(x)|² dx.
Now, consider the symmetry properties of ψ1(x) and ψ3(x). From the given relationship ψn(−x) =(−1)\((n-1)\)ψn(x), we can see that ψ1(−x) = -ψ1(x) and ψ3(−x) = ψ3(x).This implies that the integrands in the expectation value expression have opposite parity for ψ1(x) and the same parity for ψ3(x).
When integrating over an interval symmetric about the origin, such as the infinite square well, the contributions to the expectation value from functions with opposite parity cancel out. Therefore, the integral of ψ1(x) over the symmetric interval gives zero.
As a result, the expectation value ⟨x⟩ simplifies to ⟨x⟩ = (2/5)∫x|ψ3(x)|² dx. Since ψ3(x) is a symmetric function, its contribution to the expectation value remains constant with time.
Hence, ⟨x⟩ does not change with time for the given initial state Ψ(x,0)=[ψ1(x)+2ψ3(x)]/5.
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is the sum of the integers x and y a prime number? (1)x is an even prime number. (2)y is a prime number between 10 and 20.
Answers
Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.
So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.
Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.
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Jordan runs 1800 meters in 5 minutes. How many meters can Jordan run in one minute? meters per minute
Answers
Answer: 360 m/min
Step-by-step explanation:
The problem tells us he runs 1800m/5min. By dividing those numbers, we can get the unit rate.
\(\frac{1800}{5}=360 m/min\)
You can double-check if you divided the numbers correctly by looking at the units. Since you are looking for meters per minute, you divide the number of meters by the number of minutes.
!50 POINTS! (4 SIMPLE GEOMETRY QUESTIONS)
QUESTIONS BELOW:
|
|
\/
Answers
Step-by-step explanation:
Image 1:
Blank 1: (0,5)
Blank 2: (5,0)
Blank 3: (0,-5)
Blank 4: (-5,0)
Image 2:
C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.
Image 3:
B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.
Image 4:
B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.
What is the 12th term in the sequence (1,3,5,7).
Answers
Answer:
23
Step-by-step explanation:
We Know
The sequence (1,3,5,7)
Each time it increases by 2
What is the 12th term in the sequence (1,3,5,7)?
Let's list it out
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,....
So, the 12th term in the sequence is 23.
Write down the formula for the nth number and calculate the 10th number and the 101th number of the following sequence: 74, 58, 42, ...
Answers
Answer:
nth number: 74+(n-1)*(-16)
Step-by-step explanation:
A coin is tossed three times. What is the probability that the first toss and the last toss yield different outputs?.
Answers
There is a 0.5 probability that the first toss and the last toss yield different outputs.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The sample space for a coin tossed three times is:
P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}
Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.
The sample space for this is:
P = {HHT, HTT, THH, TTH}
The probability is:
\(P = \frac{4}{8} = \frac{1}{2}\)
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.
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There is a 0.5 probability that the first toss and the last toss yield different outputs.
Now, According to the question:
Let's know:
What is probability and example?
It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.
The sample space for a coin tossed three times is:
P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}
Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.
The sample space for this is:
P = {HHT, HTT, THH, TTH}
Probability = Number of Favorable Outcomes / Total Number of Outcomes.
P = 4/8 = 1/2
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.
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a person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1. find the expectation of this game. is the game fair?
Answers
A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value
How do we determine the expected value of the game?We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.
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Question 1 of 5
What is the circumference of a circle with a diameter of 6 feet? Use 3.14 for tt.
A. 18.84 ft
B. 28.26 ft
C. 37.68 ft
D. 9.42 ft
Answers
Answer:
The answer is A. 18.84
Step-by-step explanation:
Hope this helps =)
compute p(s90,000 ≤ 29, 500); express the result in decimals.
Answers
The probability of a normal distribution with a mean of 90,000 and a standard deviation of 29,500 being less than or equal to 29,500 is approximately 0.0202.
To compute this probability, we can use the standard normal distribution and transform the values accordingly:
z = (x - mu) / sigma
where:
x = 29,500
mu = 90,000
sigma = 29,500
Substituting the values, we get:
z = (29,500 - 90,000) / 29,500 = -2.0347
Using a standard normal distribution table or calculator, we can find that the probability of a value being less than or equal to -2.0347 is approximately 0.0202.
Therefore, the probability of a normal distribution with a mean of 90,000 and a standard deviation of 29,500 is less than or equal to 29,500 is approximately 0.0202.
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solve sinx = 2x-3 using false position method
Answers
The root of the equation sinx = 2x-3 is 0.8401 (approx).
Given equation is sinx = 2x-3
We need to solve this equation using false position method.
False position method is also known as the regula falsi method.
It is an iterative method used to solve nonlinear equations.
The method is based on the intermediate value theorem.
False position method is a modified version of the bisection method.
The following steps are followed to solve the given equation using the false position method:
1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.
Here, f(x) = sinx - 2x + 3.
2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))
3. Evaluate the function at point c and find the sign of f(c).
4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.
5. Repeat the steps 2 to 4 until we obtain the required accuracy.
Let's solve the given equation using the false position method.
We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.
So, the root lies between 0 and 1.
The calculation is shown in the attached image below.
Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).
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Natalie has $250 in her savings account,into which she deposits $10 of her allowance each week.The balance of her saving account can be modeled by the function f(w)=250t10w where w represents the number of weeks.Which function g(w) represents the balance of Natalie’s saving accounts if she withdraws $40 to purchase a new pair of shoes?describe the translation of f(w) that results in g(w)
Answers
If she withdraw $40 to purchase a new pair of shoes, then the function that represent her balance is g(x) = 210 + 10x
The amount that she has in saving account = $250
The amount she deposits in each week = $10
Consider the number of weeks as w
Then the function will be
f(x) = 250 + 10x
Then she withdraw $40 to purchase a new pair of shoes
Then the new function g(x) will be
g(x) = 250 + 10x - 40
Subtract the like terms in the function
g(x) = 250 - 40 + 10x
g(x) = 210 + 10x
Hence, if she withdraw $40 to purchase a new pair of shoes, then the function that represent her balance is g(x) = 210 + 10x
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angle c and angle d are supplementary angles.if the measure of angle d is 80 degress,what is the measure of angle c
Answers
Answer:
C = 100
Step-by-step explanation:
Supplementary angles equal 180 degrees
180 - 80 = 100
Answer:
m∠C = 100°
Step-by-step explanation:
Supplementary angles are angles that add up to 180°. We are given m∠D as 80°.
This means that c + 80 = 180Step 1: Subtract 80 from both sides.
\(c+80-80=180-80\) \(c=100\)Therefore, the answer is 100°.
Which number is an Rational Number?
A) 6 sqrt
B) 36/6 sqrt
C) 36/16 sqrt
D) 16/6 sqrt
Answers
Answer:
C) 36/16 sqrt
Step-by-step explanation:
\(\sqrt{6}=2.44948974...\)
The square root of 6 simplifies to a non-terminating number. It is not rational.
\(\sqrt{\frac{36}{6} } =\sqrt{6}\)
The square root of 6 is not rational, and the square root of 36/6 is equivalent to that.
\(\sqrt{\frac{36}{16} } =1.5\)
Option C is rational.
1.5 can be simplified to 1 1/2 or 3/2.
Hope this helps.
if jamie's quarterly interest payments are $150 on a $12,000 loan, then what is her annual interest rate?
Answers
Jamie's annual interest rate is 5%.
To find Jamie's annual interest rate, we need to consider the relationship between the quarterly interest payments and the loan amount. Let's break it down step by step:
1. We know that Jamie's quarterly interest payments are $150. Since there are four quarters in a year, the total annual interest payments can be calculated by multiplying the quarterly payments by four: $150 * 4 = $600.
2. Now, let's determine the interest rate. We have the annual interest payment, but we need to express it as a percentage of the loan amount. The formula to calculate interest rate is (Interest Payment / Loan Amount) 100.
3. Substituting the values into the formula, we have ($600 / $12,000)
100 = 0.05 100 = 5%.
Therefore, Jamie's annual interest rate is 5%.
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Select all pairs of angles in the figure above that are supplementaryA <1 and <7B <1 and <8C <3 and <6D <4 and <7
Answers
Solution
Notice that angle 1 and angle 8 are alternate interior angles
Hence,
\(\angle1=\angle8\)Notice that angle 8 and angle 7 are supplementary angle
Since angle 1 is equal to angle 8 it follows
Angle 1 and angle 7 are supplementary
Angle 1 and angle 3 are vertically opposite angle
Hence
\(\angle1=\angle3\)This implies that
110°
х
z
у
Find the unknown angle measures
Answers
Answer:
x = z = 70°
y = 110°
Step-by-step explanation:
From the diagram, we have 4 angles;
To find y;
110° and y are vertically opposite angles so they are equal.
So, y = 110°
Also, y and x lie on a straight line. Sum of angles on a straight line is 180°;
y + x = 180
110 + x = 180
x = 180-110 = 70°
Also, x and z are vertically opposite angles and they are equal;
x = z = 70°
y = 110°
Please help solve correctly. NO links or files. Correct answers only if not report. I will even give an additional 10 if correct.
Answers
Answer:
226.19
Step-by-step explanation:
Convert these integers from binary notation to decimal notation. a. 1 1111 b. 1 0101 0101 c. 10 0000 0001 Convert these integers from hexadecimal notation to binary notation. a. 80E b. ABBA c. 135AB Convert (7345321): to binary expansion and (10 1011 1011)2 to its octal expansion. Use Euclidean algorithm to find the god of the following: a. 12, 18 b. 1001, 1331 c. 1000, 5040 d. 111, 201 e. 12345, 54321
Answers
To convert the binary numbers to decimal:
a. 11111 (binary) = 1(2⁴) + 1(2³) + 1(2²) + 1(2¹) + 1(2⁰) = 31 (decimal)
b. 101010101 (binary) = 341 (decimal)
c. 100000001 (binary) = 257 (decimal)
To convert the hexadecimal numbers to binary:
a. 80E (hex) = 1000 0000 1110 (binary)
b. ABBA (hex) = 1010 1011 1011 1010 (binary)
c. 135AB (hex) = 0001 0011 0101 1010 1011 (binary)
To convert 7345321 (decimal) to binary, and 101011011 (binary) to octal:
(7345321)10 = 11100001011011001001 (binary)
(101011011)2 = 2533 (octal)
Using the Euclidean algorithm to find the GCD:
a. GCD(12, 18) = 6
b. GCD(1001, 1331) = 7
c. GCD(1000, 5040) = 40
d. GCD(111, 201) = 3
e. GCD(12345, 54321) = 3
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Mrs. Barlow's math class took a test yesterday. Out of 100 students, 70% of them passed. How many of Mrs. Barlow's students passed the test?
Answers
Answer:
70
Step-by-step explanation:
70 percent of 100 is \(\frac{70}{100}\)
so \(\frac{70}{100}\) × 100 students
= 70 students
A Question 7 (2 points) Retake question
Let f(x)= x + 3
The graph of f(x) is transformed into the graph of g(x) by a translation of 4 units left.
What is the equation for g(x)?
g(x) = |x-1
g(x)= |x-41 +3
g(x) = |x| +7
g(x)= x + 4 + 3
Answers
Answer:
g(x) = |x-4| + 3
solve 15 2x = 36. round to the nearest ten-thousandth.
Answers
To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.
Can any kind soul help me ASAP
Answers
2x9=18
The answer is 18 seconds.
Use the Root Test to determine if the series converges or diverges. ∑[infinity]n=1(lnn/9n−10)^n
A) Diverges
B) Converges
Answers
Series Converges using root test.
How to determine the convergence or divergence of the series?To determine the convergence or divergence of the series \(\sum[\infty n]=1(lnn/9n-10)^n\) using the Root Test, we need to compute the limit of the nth root of the absolute value of the terms.
Let's proceed with the Root Test:
Consider the nth term of the series: \(a_n = (ln(n)/(9n - 10))^n.\)Take the absolute value of the nth term: \(|a_n| = |(ln(n)/(9n - 10))^n|.\)Take the nth root of the absolute value of the nth term:\(|a_n|^{(1/n)}\)= \([(ln(n)/(9n - 10))^n]^{(1/n)}\)).Simplify the expression inside the nth root:\([(ln(n)/(9n - 10))^n]^(1/n) = ln(n)/(9n - 10).\)Compute the limit as n approaches infinity: lim(n->∞) [ln(n)/(9n - 10)].To evaluate this limit, we can use L'Hôpital's Rule. Differentiating the numerator and denominator with respect to n gives:
lim(n->∞) [ln(n)/(9n - 10)] = lim(n->∞) [1/(9n - 10)] / (1/n).
Simplifying further:
lim(n->∞) [1/(9n - 10)] / (1/n) = lim(n->∞) [n/(9n - 10)].
Dividing both the numerator and denominator by n yields:
lim(n->∞) [n/(9n - 10)] = lim(n->∞) [1/(9 - 10/n)] = 1/9.
Since the limit is a finite non-zero value (1/9), the Root Test tells us that if the limit is less than 1, the series converges. If the limit is greater than 1 or infinity, the series diverges.
In this case, the limit is 1/9, which is less than 1. Therefore, the series ∑[infinity]n=\(1(lnn/9n-10)^n\) converges.
Therefore, the correct option is:
B) Converges
So, Series converges
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