Chapter 11.2, Problem 78E

Graph the curves $y=x^n$, $0\le x\le 1$, for $n=0,1,2,3,4,\mathrm{...}$ on a common screen. By finding the areas between successive curves, give a geometric demonstration of the fact, shown in Example 8, that

${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{n\left(n+1\right)}}=1$