If E Un is absolutely convergent then (un)² is also n=1 n=1 convergent.

Q: E Suppose we also know that 1 > an > 0. and a converge. Then the series > converge 1-an Select one:…

A:

Q: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >…

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to…

Q: a) Determine if Eº, absolutely converges, conditionally converges, or diverges. ´n=2 n-yn

A:

Q: 1 is not convergent. Theorem 1.8.2 E n = 1

A:

Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: The series True False 80 n=1 (-1) n is conditionally convergent.

A: The given series is ∑n=1∞-1nn. The objective is to check whether the given series is conditionally…

Q: 52n 5n +1 n=1

A: Given that:- ∑n=1∞52n5n+1To find:- chek whather the series is convergent or divergentSolution:-limit…

Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

A:

Q: Supposean converges conditionally (but not absolutely). Let A+ = {n €N : an ≥ 0} n=0 and A_ = {n € N…

A:

Q: The series > (2)k-1 converges. k=1 Select one: True O False

A:

Q: 7N 8N 3) Show that converges/diverges.

A:

Q: The following series Σ 3n-2" 5n+1 n=0 is convergent to

A: this is convergent series and

Q: The series 7 2n E,(-1)" 4 n= is absolutely convergent. Select one: True O False

A: Root Test : Suppose we have series ∑ an .Define,                          L = limn→∞ an1n .Then ,(…

Q: Determine if >n=1 (-1)" is absolutely convergent or conditionally divergent. 4n 4 +1

A: First check for Absolutely convergence using Series Integral Test

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

A:

Q: Š V2n-5 n=1 n2- 3n +4

A:

Q: The infinite series 1)* is convergent. k-1 a) true b) false

A: The given series is an alternating series.

Q: Find the sum of the convergent series. +0 | 3n+1 6n-1 n=0

A:

Q: (- 1)"+(- =D1 converges conditionally in elect one: True

A: Please refer to the image below

Q: An alternating p-series 1 n=1 is absolutely convergent for p >1 p > 1 0 0

A:

Q: Find the sum of the convergent series.

A:

Q: d) Determine whether ) (an + bn) is convergent or divergent. n=1

A:

Q: n2 + 5n + 2 Determine whether converges abso- (1+ )" lutely, converges conditionally, or diverges.…

A:

Q: The series 2(k+2)3-k is k=1 convergent to 6 divergent convergent to 8 O None 15 convergent to 2

A: Given - A series To find - Nature of Series , i.e. Convergence or Divergence

Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

A:

Q: e-n n(n + 1) E(-1)"+1. n=l

A:

Q: Show that if $a_{n}>0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an > 0 and series is convergent. We need to prove that: is convergent.…

Q: If {fn}n=1 is a pointwise convergent, then {fn}=1 is uniformly convergent.

A:

Q: A. Determine the convergent of the following series. 1- Vn(Vn+1)

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: The series 1 Σ 2 (-1) "-1. 00 n=1 1.8 is absolutely convergent. Select one: O True O False

A:

Q: , 2η En=1 3 er

A: Given series is ∑n=1∞ n2nen3. Here, an=n2nen3.

Q: - 1)n+'] (a) Converges to Diverges .......... 5"

A:

Q: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

A:

Q: establish whether it is conditionally convergent, absolutely convergent or divergent sum n=1 to ∞…

A:

Q: a) [*. : Determine whether the series 1 Σ (2n – 1)4 n =1 is convergent or divergent.

A: To determine whether the given series is convergent or divergent

Q: If both E Un and E(-un) converges then E Un| n=1 n=1 n=1 is also convergent.

A: It is given that ∑n=1∞un and ∑n=1∞-un converges.

Q: ind the sum of the convergent series. +00 3n+1 Z 6n-1 n=0

A:

Q: ca, is convergent. is an convergent and c is a nonzero constant, then If n=1 n=1

A:

Q: Suppose {fn}n=1 converges uniformly on E. Show {fn}n=1 converges pointwise on E.

A:

Q: Consider an = V4n² + 3n – 2n for n > 1. (a) Determine if {an}-1 is convergent or divergent n=1 (b)…

A: a) Given an = 4n2+ 3n   -2n Rationalize (4n2+ 3n  - 2n) (  4n2+ 3n  +  2n) (  4n2+ 3n  +  2n) = (…

Q: If possible, give an example of 2 convergent sequences an and bn such that E(an + bn) diverges.

A:

Q: IV. Determine if the given is convergent or divergent. s In"(n*) 23n2 #4. n=1

A: Given series is ∑n=1∞lnn(n4)23n2

Q: Find the sum of the convergent series. 1 n vn + 1. n=16

A:

Q: N + 1 2N 2) Show that converges/diverges. N-1

A: The given series is: ∑N=1∞N+12N+1 Let. aN=N+12N+1,N≥1

Q: 1 Show that the series 2 converges. k=2 k(log k)?

A: Given: ∑k=2∞1klogk2

Q: Σ (-1)** In+15 a. Absolutely Convergent b. Conditionally Convergent с. Divergent

A: We have to check

Q: Prove that the sequence {sin(nn/3)} does not converge.

A:

Q: 6n2 n

A: The given sequence be 6n2en To find it is convergent or divergent

Q: Show that if

A: x+y≤x+y