Use series you know to show that:

1 - 1/3 + 1/5 - 1/7 + ... = pi/4

I get that arctanx = x - 1/3x^3 + 1/5x^5 - 1/7x^7

and arctan 1 = pi/4

but I'm not sure how I'm supposed to show this; what is the connection? Is this the connection I am looking for?