Graph the curves y = xn, 0 ≤ x ≤ 1, for n = 0, 1, 2, 3, 4, . . . on a common screen. By finding the areas between successive curves, give a geometric demonstration of the fact, shown in Example 2, that

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1 1 1 1 1 + ... + Sn %3| 司 i(i + 1) 1:2 2.3 3.4 п(п + 1) 00 1 Σ 1 =1 n(n + 1) ||