Hey guys, I have an important question to ask. Suppose you have a power series, for instance (x^n)/n+3, with n running from 0 to infinity, and you want to calculate the function S(x) (obviously, in [-1,1), where the convergence is uniform). What I do is to take out of the series 1/x^3, so that I can derive the series in order to get a geometrical series etc. etc. etc.
My question is: do I find the derivative of the series or the derivative of 1/x^3 times the series? I think I should derive only the series, my friend says the opposite...

Question

Hey guys, I have an important question to ask. Suppose you have a power series, for instance (x^n)/n+3, with n running from 0 to infinity, and you want to calculate the function S(x) (obviously, in [-1,1), where the convergence is uniform). What I do is to take out of the series 1/x^3, so that I can derive the series in order to get a geometrical series etc. etc. etc.
My question is: do I find the derivative of the series or the derivative of 1/x^3 times the series? I think I should derive only the series, my friend says the opposite...

irishboy123 · Answer

@freckles @ganeshie8

anonymous · Answer

$$1/ x ^{3} \sum_{0}^{\infty}x ^{n+3}/(n+3)$$
This is the damn thing I should derive, do I have to derive it all or just the series?
(Thank you IrishBoy :D)