Suppose I have a series $\sum a_n$ that is absolutely convergent. How to show that $\sum a^2_n$ is convergent? I can imagine this to be true, but I'm not sure how to prove it mathematically.
Series Convergence
2
$\begingroup$
real-analysis
1 Answers
13
Hint: Eventually, |a_n|<1, and then $0\le a_n^2\le|a_n|$. Use a comparison test.