Evaluate the infinite sum ∑n=0∞(−1)nn!⋅2n\sum_{n=0}^{\infty} \frac{(-1)^n}{n! \cdot 2^n}∑n=0∞n!⋅2n(−1)n.
e−1e^{-1}e−1
e−1/2e^{-1/2}e−1/2
e1/2e^{1/2}e1/2
1−e1 - \sqrt{e}1−e