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# Taylor series (doing something wrong!) watch

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1. Hey,

the question first asks me to find the taylor expansion of 1/(1-x) by differentiating successively at x=0.

I've done that and obtained the following: 1 + x + x2 + x3 + .......

This is the next part of the question:

b) Use this to find the Taylor expansion for arctan z about z=0 (Hint: recall d/dz (arctan z) = 1/ (1+ z2) and so substitute x= -z2 into the expansion of part a.)

I've substitued x=... into my first expansion but I get: 1 - z2- z4- ........

I know this is not right, because I've done it the long way, but what am I doing wrong?

2. d/dz(arctan z)=1/(1+z^2)

Let x = -z^2

and you get 1 - z^2 + z^4-... from part a) which is where youre going wrong by the looks of it.

Then integrate term by term to get

arctan z = z -1/3z^3+ 1/5z^5
3. No problem

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