Determine the value of the infinite sum ∑n=0∞(−1)nπ2n+142n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n \pi^{2n+1}}{4^{2n+1} (2n+1)!}∑n=0∞42n+1(2n+1)!(−1)nπ2n+1.
12\frac{1}{2}21
22\frac{\sqrt{2}}{2}22
111
32\frac{\sqrt{3}}{2}23