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Hi everyone, I am completely stuck on the below problem. Would anyone like to give me a hint?

This is the problem:

Let

f(x) = \sum {a(i)*x^(i)}

for i=0 up to infinity

given that f(0)= 0 , find the first three terms in the Taylor expansion about

x = 0 of the function [tex]1/f(x)[/tex] .

Thanks a lot!

PS: also, for the expansion of [tex]e^{e^(x)}[/tex] is it OK to simply expand the entire function in one go by differentiating the entire thing (which is what I did) or does one have to split it up somehow?

This is the problem:

Let

f(x) = \sum {a(i)*x^(i)}

for i=0 up to infinity

given that f(0)= 0 , find the first three terms in the Taylor expansion about

x = 0 of the function [tex]1/f(x)[/tex] .

Thanks a lot!

PS: also, for the expansion of [tex]e^{e^(x)}[/tex] is it OK to simply expand the entire function in one go by differentiating the entire thing (which is what I did) or does one have to split it up somehow?

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