Question

sum the power series
x + sum (-1)^-n (1.3.5....(2n-1)/2.4.6...2n.(2n+1)) x^(2n+1) where n goes from 0 to infinity and absolute(x) < 1.

Answer 1

it is same as
\[x + \sum_{0}^{\infty} (-1)^{n} x ^{2n+1}((1.3.5....(2n-1))\div(2.4.6....2n.(2n+1)))\]
where \[\left| x \right| < 1\] and \[x \in R\]