Answer by Julián Aguirre for Convergence of...
If $\sum a_n<\infty$ then$$\sum\frac{a_n}{1+a_n^2}\le \sum a_n<\infty.$$Suppose now that $\sum a_n$ diverges. If $a_n$ is bounded, that is, $a_n\le M$ for some $M$,...
View ArticleConvergence of $\sum^\infty_{n=1}\frac{a_n}{1+a_n^2}$
We have a positive series $\displaystyle\sum^\infty_{n=1}a_n$. is the following series converge or diverge ?$$\displaystyle\sum^\infty_{n=1}\frac{a_n}{1+a_n^2}$$...
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