Determine whether ∞∑n=1e1/n n2 converges or diverges.

Q: Does diverge? If it converges, find the value. xe da converge or

A: ∫0∞xe-x2dx

Q: - Find the interval of convergent for : 2n 2 2n! n=0

A:

Q: Decide whether the following converges or diverges. Ln=1 Inn+n/2

A:

Q: Find the sum of the convergent series.

A:

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: How to determine nln(n)/(n+1)^3 is convergent or divergent?

A: To determine the sum of the series nln(n)/(n+1)^3 is convergent or divergent. Now, Apply the…

Q: Sn(x) = e-(2-n)a

A: Given that, fnx=e-x-n2 To show that the given function is uniform convergence at [-1,1]. Let,…

Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-

A:

Q: Use the definition to show that dx 2x2 converges.

A: We have to show that the given integration converges.…

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: dx Study the convergence of 1= Solution

A:

Q: +oo Σ 8n2 16n + 6

A:

Q: Prove the absolute value of this series converges.

A: Given series :

Q: 2) is E=1 2n convergent?

A:

Q: 2n + 5 9n + 4 n=1

A:

Q: Show that the series Σ (-1)"+1 log(n + 1) converges.

A:

Q: The sequence Converges to e Diverges Converges to 0 Converges to 2e Converges to 1

A: First I have written the definition ofconvergent and divergent sequence and then that given sequence…

Q: 00 k6 k! k=1

A: We have to apply the ratio test to the following series -  ∑k=1∞k6k!

Q: Find the sum of the convergent series by using a well-known function. Identify the function and…

A: Given series is ∑n=0∞-1n12n+1......(1) We have a well known function  ∑n=0∞-1nx2n+12n+1=tan-1x,…

Q: Gk=0

A:

Q: (-1)" (2n)! 27 En=1

A: The series is given by ∑n=1∞-1n2n!2n To determine: The convergence of the series using Series Ratio…

Q: 3. The numerical series log O converges to a ptive number O diverges to+0. Odiverges to-0. O…

A: We can find whether the given numerical series converges or diverges using limit comparison test.

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: Determine whether r{(1+E)*"}.. Converges or diverges.

A:

Q: The series E=1 is convergent. 1+(" Select one: O True False

A: ∑n=1∞ 21+34n

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: ∫0∞eax dx converges for a<0. Now, ∫0∞eax dx=eaxa0∞=1ae-∞-e0=1a0-1=-1a

Q: The sequence Converges to e Diverges Converges to 2e Converges to 1 Converges to 0

A:

Q: How do I determine if this converges to a certain value, or diverges without bound?

A:

Q: Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen…

A:

Q: What is the convergency interval of (2n)l

A: The given series is,  ∑n=1∞n!23n2n!xn To find its interval of convergence.

Q: The sequence {x}=0, where xn 20" is convergent.

A:

Q: Σ converges/diverges N! 9) Show that

A: Ratio test

Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

A:

Q: n=1 3n11 Int1

A:

Q: Find the sum of the convergent series. Σ 4 5 n = 0

A: Sum if given convergent series is 45.

Q: n sin"(n) :) has a convergent subsequence. Vn2+2n Show that (an) = (-

A: Consider the sequence an=nsinnnn2+2n We have to show that sequence an has a convergent subsequence.…

Q: Sin () fan--() absolutely Converyent, conditionally convergent E (-)" fonverget ardiver Calm or…

A: follow next step

Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges

A:

Q: =) Show that converges/diverges n-1

A:

Q: 7n+2 5. By using Ratio Test, determine whether > converges or diverges. (n + 1)! n=1

A: The answer is found in step-2

Q: Determine whether ∞∑n=1n√3 converges or diverges.

A: The given series is Now, the nth term of series is

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

A:

Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

A:

Q: Find a power series representation for f(x) = In(1 – x) and give the interval of - convergence.…

A:

Q: Test the Convergencyo4 Ź tan (hn)

A:

Q: n! Determine whether E- converges or diverges. Zn=0

A:

Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

A:

Q: cos" (;) is absolutely convergent, conditionally convergent, or divergent. en?

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.