Question

Which of the following is true regarding the series ∑nr=1e1−r

Hint: write out the first few terms of the series to understand it better


A. This series is not a geometric series.

B. ∑r=1ne1−r=en−1e−1

C. limn→∞∑r=1ne1−r=ee−1

D. The series is a telescoping series

Answer 1

A) this series is a geometric series: $a=1;q=e^{-1}$ - false

B) For the geometric series $S_n=\frac{a(1-q^n)}{1-q}$ therefore $S_n=\frac{1-e^{-n}}{1-e^{-1}}$

C) $\lim\limits_{n\to\infty}S_n=\frac{1}{1-e^{-1}}=\frac{e}{e-1}$ - true

D) this series is not a telescoping series