Finding Power Series Representation for arctan(x): Help Needed!

[teng125]

may i know how to solve this ques:find the power series representation for arctan (x)

i know that arctan (x) = integ 1/(1 + x^2) but then from here i don't know how to continue.
pls help...

 

[Hurkyl]

It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.

 

[teng125]

ya I'm looking for the thing on the left hand side...pls help

 

[finchie_88]

Take the thing on the right, and differentiate it a few times, and let x = 0 each time.

$$f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + ...$$

Where f'(0) represents the derivative at x = 0. f''(0) is the second derivative etc. This will give a power series, then you can integrate term by term for the inverse tan function.

 

[Hurkyl]

One doesn't need to know any calculus at all to find the power series for $1/(1+x^2)$.

ya I'm looking for the thing on the left hand side...pls help

I gave you a big hint -- have you not tried to do anything with it?

 

[HallsofIvy]

ya I'm looking for the thing on the left hand side...pls help

Go back and read Hurkyl's reply again!

It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.