How can I find the limit of the series $\sum^{\infty}_{n=0} \frac {(-1)^n 2^{-n} x^{2n+1}} {n!}$?
How can I find the radius of convergence $R$ of the power series $\sum^{\infty}_{n=0} \frac {(-1)^n 2^{-n} z^{2n+1}} {n!}$?