1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite series question

  1. Apr 4, 2010 #1
    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
  2. jcsd
  3. Apr 4, 2010 #2
    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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook