Chapter 5.3, Problem 179E

In the following exercises, find a value of N such that $R_N$ is smaller than the desired error. Compute the

corresponding sum ${\displaystyle \underset{n=1}{\overset{N}{\sum }}{a}_n}$ and compare it to the given estimate of the infinite series.

179. $a_n=\frac{1}{e_n},\text{error}{\text{<10}}^{\text{-5}},{\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{e^n}=\frac{1}{e-1}=\mathrm{0.581976...}}$