Deriving the Power Series of Arctan through Integration

hivesaeed4
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How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.
 
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hivesaeed4 said:
How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.


\frac{1}{1+x^2} = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-..., and since

(Arctan\, x)'=\frac{1}{1+x^2} , then...

DonAntonio
 
hivesaeed4 said:
How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.

Hey hivesaeed4 and welcome to the forums.

To add on to what DonAntonio said, investigate what Taylor series are and how are they are used:

http://en.wikipedia.org/wiki/Taylor_series
 
Thanks. Thanks alot.
 

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