Welcome to our community

Be a part of something great, join today!

Problem of the Week #362 - January 5, 2021

  • Thread starter
  • Moderator
  • #1

Euge

MHB Global Moderator
Staff member
Jun 20, 2014
1,905
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!