# Thread: Convergence, Divergence of a series

1. ## Convergence, Divergence of a series

For the following series, determine its convergence or divergence. If it converges, find its sum:

a) $\sum_{n=2}^{\infty} \frac{1}{n^2-1}$ converges to $0$

b) $\sum_{n=1}^{\infty} \frac{n+1}{2n-1}$ diverges

c) $\sum_{n=2}^{\infty} \frac{n}{ln (n)}$ diverges

2. Originally Posted by qzno

For the following series, determine its convergence or divergence. If it converges, find its sum:

a) $\sum_{n=2}^{\infty} \frac{1}{n^2-1}$ converges to $0$

b) $\sum_{n=1}^{\infty} \frac{n+1}{2n-1}$ diverges

c) $\sum_{n=2}^{\infty} \frac{n}{ln (n)}$ diverges

(b) and (c) are ok ... the sum of (a) is not 0.

$\sum_{n=2}^{\infty} \frac{1}{n^2-1} = \frac{1}{2} \sum_{n=2}^{\infty} \frac{1}{n-1} - \frac{1}{n+1} = \frac{3}{4}
$