f(x)=1+x+x^2+x^3+...+x^n=(1-x^(n+1))/(1-x)
f'(x)=1+2x+3x^2+4x^3+...nx^(n-1)=[(1-x^(n+1))/(1-x)]'=((n (x-1)-1) x^n+1)/(x-1)^2
f'(2)=(n-1)*2^n+1