• Support PF! Buy your school textbooks, materials and every day products Here!

Infinite series question

  • Thread starter fjotlandj
  • Start date
  • #1
1
0
Given that the series from n = 1 to infinity of An converges to L, which of the following conclusions is valid for the series from n = 1 to infinity of (An)^2?

A) It may diverge
B) It converges absolutely
C) It converges to M < L
D) It converges to M > L
E) It converges to M^2 = L

My intuition tells me the answer is E). But I am not sure can someone help figure this out please
 

Answers and Replies

  • #2
179
2
Given that the series from n = 1 to infinity of An converges to L, which of the following conclusions is valid for the series from n = 1 to infinity of (An)^2?

A) It may diverge
B) It converges absolutely
C) It converges to M < L
D) It converges to M > L
E) It converges to M^2 = L

My intuition tells me the answer is E). But I am not sure can someone help figure this out please
Hints: convergent geometric series (this should eliminate some of the possible answers). Then look up what it means to converge absolutely, and play around with

[tex]\sum_{n=1}^\infty \frac{(-1)^{n+1}}{\sqrt{n}}[/tex]
 

Related Threads for: Infinite series question

  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
354
  • Last Post
Replies
1
Views
790
Replies
3
Views
1K
Replies
1
Views
1K
Top