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Derivative of power series

I have a function defined as a power series. I'm to show that f(0) = 0, and that f'(0) = 1.

f(0) is obviously = 0, but when I take the derivative, what I get seems to also be equal to 0, not 1. Did I do the derivative wrong, or should this really equal 1?

Thanks!

Re: Derivative of power series

Your derivative seems correct, I cannot see anything wrong with what you have written. 0 raised to the power of anything (except zero) equals zero and so the numerator will always be zero and the summation will just be a sum of zeros which will equal zero. Maybe you wrote down the question incorrectly?

Re: Derivative of power series

Nevermind I made a mistake

EDIT: The derivative is actually $\displaystyle \displaystyle{\sum_{n=0}^{\infty} \frac{(4n+1)z^{4n}}{(4n+1)!}}=1+\displaystyle{\sum _{n=1}^{\infty} \frac{(4n+1)z^{4n}}{(4n+1)!}}$