# Series - Properties of convergent series

Convergent Series : $\displaystyle \sum_{n=1}^\infty a_n= A , \displaystyle \sum_{n=1}^\infty b_n= B$

Real NUmber : c

1. $\displaystyle \sum_{n=1}^\infty(a_n+b_n)=\displaystyle \sum_{n=1}^\infty a_n+\displaystyle \sum_{n=1}^\infty b_n=A+B$
2. $\displaystyle \sum_{n=1}^\infty ca_n= c \displaystyle \sum_{n=1}^\infty a_n= cA.$