Mathematics

Problem

The Maclaurin series for

\arctan x

\displaystyle \arctan x=\sum_{n=0}^{\infty}(-1)^n\dfrac{x^{2n+1}}{2n+1}

for

|x|\le 1,\;x\ne\pm 1

. Determine a power series representation for

\dfrac{1}{1+x^{2}}

and state its radius of convergence.