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Problem of the Week #362 - January 5, 2021

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MHB Global Moderator
Staff member
Jun 20, 2014
Happy New Year everyone! Here is this week's POTW:

If $\sum a_n$ is an absolutely convergent series of nonzero real numbers, prove that $\sum \dfrac{a_n^2}{1 + a_n^2}$ converges. If, in addition, $a_n \neq -1$ for all $n$, show that $\sum \dfrac{a_n}{1 + a_n}$ converges absolutely.


Remember to read the POTW submission guidelines to find out how to submit your answers!