Is there a way to check if a power series representation of a function is correct?
The power series is x+2x^2+3x^3+... The derivative of that at x=0 is most certainly 1. What went wrong with your reasoning above?Ok f(0) = the value of the power series at x=0
The first derivative of the function is (-x^2 + 1)/(1-x)^4 so f'(0)=1
The first derivative of the power series is sum from n=1 to infinity of n^2*x^(n-1) and if I plug in x, I will get zero. What am I not understanding?