Series - Binomial series

Whole numbers : n, m
Real number : x
Combinations : \(^nC_m\)

 

  1. \((1+x)^n=1+^nC_1x+^nC_2x^2+...+^mC_nx^m+...+x^n\)
  2. \(^nC_m={n(n-1)...[n-(m-1)] \over m!},|x|< 1.\)
  3. \({1 \over 1+x}=1-x+x^2-x^3+...,|x|<1.\)
  4. \({1 \over 1-x}=1+x+x^2+x^3+...,|x|<1.\)