Problem 78E

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

$$\sum_{n=1}^{\infty} \frac{1}{n(n+1)}=1$$

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