- #1

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## Homework Statement

Show the convergence of the series

[tex] \sum_{n=1}^{inf}(\frac{1}{n}-\frac{1}{n+x})[/tex]

of real-valued functions on [tex] R - \{-1, -2, -3, ...\} [/tex].

## Homework Equations

## The Attempt at a Solution

I first thought of solving this using telescoping series concept but it didn't work out. Also, I tried to prove it by saying that since denominator goes [tex]n^2[/tex] it should converge but what I doubt is that the elements of the series change sign and the modulus of its terms will not be lower than [tex]1/n^2[/tex].