# Series - Infinite series

Sequence :{ ${a_n}$

First term : $a_1$

$N^{th}$ term : $a_n$

1. Infinite Series
$\displaystyle \sum_{n=1}^\infty a_n =a_1+a_2+...+a_n+...$
2. $N^{th}$ Partial Sum
$S_n = \displaystyle \sum_{n=1}^n a_n =a_1+a_2+...+a_n$
3. convergence of Infinite Series
$\displaystyle \sum_{n=1}^\infty a_n = L, \; if \; \displaystyle\lim_{n \to \infty} S_n=L$
4. $N^{th}$ Term Test
*  If the series $\displaystyle \sum_{n=1}^\infty a_n$ is convergent , then $\displaystyle\lim_{n \to \infty} a_n=0,$
*  If $\displaystyle\lim_{n \to \infty} a_n \ne0,$ then the series is divergent.