0
$\begingroup$

Let $p \geqslant 1$ and let $(a_n)$ be a sequence of non-negative numbers. Then if $\sum\limits_{n=1}^\infty a_n$ converges, so does $\sum\limits_{n=1}^\infty a_n^p$. Prove this statement.

Sorry, we have just started learning series in class, but I have this homework problem and can't get anywhere. Any help/hints appreciated!

$\endgroup$
2
$\begingroup$

Eventually, $a_n<1$, then $a_n^p<a_n$ so...?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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