Chapter 3.1, Problem 23E

It can be shown that the number e satisfies the inequality

  $\begin{array}{rr}\hfill {\left(1+\frac{1}{n}\right)}^n<e<{\left(1+\frac{1}{n}\right)}^{n+1}& \hfill n\ge 1\end{array}$

Illustrate this condition by graphing

  $\begin{array}{lll}{y}_1\hfill & =\hfill & {(1+1/n)}^n\hfill \\ y_2\hfill & =\hfill & 2.718281828\approx e\hfill \\ y_3\hfill & =\hfill & {(1+1/n)}^{n+1}\hfill \end{array}$

in the same viewing window, for 1 ≤ n ≤ 20.