A power series representation of that converges for is

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

A power series representation of

\displaystyle \frac{1}{1+x^{2}}

that converges for

|x|<1

\sum_{n=0}^{\infty}(-1)^n x^{2n}

. Find a power series representation for

\arctan x

satisfying

\arctan 0=0

, and determine the interval of convergence.