High school Calculus homework on series

[snowlove]

high school Calculus B/C class homework:

1) Find a Series for f(x) = $$\frac{1}{1+x}$$ then find the interval of convergence.

i know that $$\frac{1}{1+x}$$ = 1-x+ $$x^{2}$$-$$x^{3}$$+...+ $$-x^{n}$$+... -1<x<1
but then i don`t understand how can i use the result from 1) to find 2) answer? since you guy will teach me how to do 2) then do i just do the same thing for 3) ?

2) Using your result from 1) find a series for $$\frac{1}{1+x^2}$$

3) Using your result from 2) find a series for $$tan^{-1}x$$ then use your series to approximate $$\pi$$ to four decimal places. How many terms did you need?

 

[rock.freak667]

Replace x by x²

For the third one, consider what d/dx(tan^-1x) gives

 

[snowlove]

thank you