Evaluate the infinite sum: ∑n=1∞ne−n\sum_{n=1}^{\infty} n e^{-n}∑n=1∞ne−n
e(e−1)2\frac{e}{(e-1)^2}(e−1)2e
1(e−1)2\frac{1}{(e-1)^2}(e−1)21
ee2−1\frac{e}{e^2 - 1}e2−1e
1e(e−1)2\frac{1}{e(e-1)^2}e(e−1)21