Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Series convergence proof?
Sum of (-1)^k (3/2^k) 0 to infinity
I know the series converges to 2, I just don't know how to do the proof
1 Answer
- Anonymous1 decade agoFavorite Answer
Note that:
∑ [(-1)^k * 3/(2^k)] (from k=0 to infinity)
= 3 * ∑ (-1)^k/2^k (from k=0 to infinity)
= 3 * ∑ (-1/2)^k (from k=0 to infinity).
This series is now a geometric sequence with a common ratio of -1/2. So:
∑ (-1/2)^k (from k=0 to infinity) = 1/[1 - (-1/2)] = 1/(3/2) = 2/3.
Therefore, ∑ [(-1)^k * 3/(2^k)] (from k=0 to infinity) = 3(2/3) = 2 as required.
I hope this helps!