Determine whether each of the following series is absolutely convergent, conditionally convergent on divergent. Show all necessary steps.

Q: u) 1 Σ(-3 ---) n

A: Convergence of the series is tested by using comparison test

Q: Give an example to show that a convergent series sum⟨x,ek⟩ek does not haveto sum to x.

A: First, let's understand the concept. A convergent series is a series whose partial sums eventually…

Q: Determine whether the series is convergent or divergent. If it is convergent, n2 n=1 how many terms…

A: To find- If the given series is convergent.

Q: Find the sum of the convergent series 8-1+- O 512 64 318

A:

Q: 1 is convergent, and find its sum. Show that the series n(n + 1) n=1

A: we have to show that the given series is convergent and then we have to find the sum. ∑n=1∞1n(n+1)

Q: State whether each graph is an even, odd, or neither even nor odd function -3m/2 ---m2 |3m2 2= even…

A: The graph of an odd function is symmetric about the origin. The graph of an even function is…

Q: = {()}. 2n 1 2n +1) T2 a) {a,} -

A: Given: To determine the series converges or diverges as follows, an=2n-12n+1n

Q: Show that X is complete if and only if every absolutely convergent series in X converges.

A: To Show : X is complete if and only if every absolute convergent series in X converges.

Q: Show whether each of the following series and sequences converges or diverges. If convergent, enter…

A: Divergent test : If limk→∞ ak ≠0 then ∑k=1∞ ak is divergent .

Q: Give an example of a conditionally convergent series an such that Σna, con- n=1 n=1 verges.

A:

Q: 00 n 2 Does the seriesE (- 1)"n²| | converge absolutely, converge conditionally, or diverge? 3 n= 1…

A: Consider the series ∑n=1∞−1nn223n We have to check whether the given series is converges absolutely,…

Q: Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction…

A:

Q: In 3n an = In 5n

A:

Q: +5 St su

A:

Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

A: Given that : The series ∑n = 1∞ 1n .

Q: Determine whether the sequence (3n)/(4n-1) converges or diverges. Show all necessary  calculations…

A: Given an=3n4n-1