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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. \(\displaystyle \sum_{n=1}^\infty ca_n= c \displaystyle \sum_{n=1}^\infty a_n= cA.\)