Math Help - Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

1. Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

Given the infinite series xn is absolutely convergent, show that the infinite series xn/(1+xn) is absolutely convergent.

I am completely stumped, I have tried using properties of the limit test and the comparison test to show this, but I can't seem to make any progress,

2. Re: Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

Since the series $\sum_n |x_n|$ is convergent, we have in particular that $|1+x_n|\geq \frac 12$ for $n$ large enough. Hence we have $0\leq \left|\frac{x_n}{1+x_n}\right|\leq 2|x_n|$, and you can conclude.