Just as with the series representation of ln(1+x) we would start with a geometric series and integrate both sides. The details are left to you .... the boundary points |x| = 1 are an application of Abel's Limit theorem, which you should be able to do as well.

	f(x) = arctan(x)

Since tan(/4) = 1 we have arctan(1)=/4. Thus, this statement follows from the above representation for x = 1.

Series approaching Pi/4=0.785398