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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.

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1 Answer 1

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

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