Find the associated radius of convergence, R.

For the sum from n = 0 to infinity of (-1)^(n) *(pi^(2n+1))/((2n+1)!) *(x^(2n+1))

If a_n is the abs val. the ratio test gives you a_n+1/a_n = (pi)^2* IxI^2/ (2n+2)(2n+3)==>0
so the series is absolutely convergent for all x and so the radius of convergence is infinity