Deriving the Power Series of Arctan through Integration

[hivesaeed4]

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.

 

[DonAntonio]

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

 

[chiro]

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

 

[hivesaeed4]

Thanks. Thanks a lot.