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.