Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question

Hint: Eventually, $|a_n|<1$, and then $0\le a_n^2\le|a_n|$. Use a comparison test.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.