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.

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# Series Convergence

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