Determine the sum of the series $\mathrm { e } ^ { - 1 }$ + $e ^ { - 2 }$ + $\mathrm { e } ^ { - 3 }$ + ... if it converges.
A) diverges
B) $\frac { 1 } { e - 1 }$
C) $\frac { e } { e - 1 }$
D) e

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = e^{-1}$ and common ratio $r = e^{-1}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting the values, we get $S = \frac{e^{-1}}{1 - e^{-1}} = \frac{1}{e - 1}$.

Determine the Sum of the Series e−1\mathrm { e } ^ { - 1 }e−1

Determine the Sum of the Series $\mathrm { e } ^ { - 1 }$