Question

# Please justify whether the series converges or diverges, and find sum, if it converges. sum_(n = 1)^ oo 3/n^2

Series
Please justify whether the series converges or diverges, and find sum, if it converges.
$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}$$

2021-09-03

$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}$$
$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{p}}}$$ – if $$\displaystyle{p}{>}{1}{Z}$$ – series converges, if $$\displaystyle{p}{<}{1}$$, series diverges.
Therefore, series converges by p-test.

2021-09-23