How Do You Find the First Three Terms of 1/f(x) and Expand e^e^x?

[mmh37]

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 $$1/f(x)$$ .

Thanks a lot!

PS: also, for the expansion of $$e^{e^(x)}$$ 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?

 

[arildno]

Improve your notation first.

 

[mmh37]

I tried to do it with latex but I don't know how to do sums? And strangely if I put Latex brackets around the first expression it generates a different image,namely $$exp^{exp^{x}}$$, instead of the sum formula. This is all very odd!