Given [tex]a_{n} > 0[/tex] and [tex]\sum a_{n}[/tex] diverges, show that [tex]\sum \frac{a_{n}}{1+a_{n}}[/tex] diverges.(adsbygoogle = window.adsbygoogle || []).push({});

Since I don't have an explicit form for the series, I can't apply any of the standard tests. I'm not sure where to start on this problem. I know the criteria for convergence/divergence, namely tail end of series has to converge or cauchy criterion condition. But I don't see how that helps without knowing what series looks like. Please steer me in the right direction.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Series Convergence

**Physics Forums | Science Articles, Homework Help, Discussion**