# Tell whether the series converges or diverges, and find sum, if it converges.

Tell whether the series converges or diverges, and find sum, if it converges.
$$\displaystyle{\sum_{{{n}={3}}}^{\infty}}{\left(\frac{{1}}{{{n}–{2}}}–\frac{{1}}{{n}}\right)}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

averes8

$$\displaystyle{\sum_{{{n}={3}}}^{\infty}}{\left(\frac{{1}}{{{n}–{2}}}–\frac{{1}}{{n}}\right)}$$
$$\displaystyle{\sum_{{{n}={3}}}^{\infty}}\frac{{1}}{{{n}\times{\left({n}-{2}\right)}}}$$
This is not geometric series
$$\displaystyle{S}_{{n}}={1}+\frac{{1}}{{2}}=\frac{{3}}{{2}}\ {a}{s}\ {n}\to\infty.$$
Thus, series converges.