Maclaurin series for arctan

My method:

Assume the McSeries is known;
Differentiate it, and equate it to the derivative of arctan(x);
Multiply through both sides by (1+x²);
On one side, a series involving terms with increasing powers of x, while on the other side, a short series -- 1!
In order to be equal, they must have equal coeffients; equate them, and you'll find a recurrence relation to solve for the coefficients.

Website maintained by Andy Long. Comments appreciated.