let
g(x)= 1/(1+x) => g(0) =1
g'(x) = -1/(1+x)^2 =>g'(0)/1! =-1
g''(x) = 2/(1+x)^3 =>g''(0)/2! =1
...
g^(n)(x) = (-1)^n. n!/(1+x)^(n+1) =>g^(n)(0)/n! =(-1)^n
1/(1+x)
=g(x)
=g(0)+[g'(0)/1!]x +[g''(0)/2!]x^2+....+[g^(n)(0)/n!]x^n+...
=1-x+x^2+....+(-1)^n. x^n +....
x=2x
1/(1+2x)=1-(2x)+(2x)^2+....+(-1)^n. (2x)^n +....
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