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Today's calculation of Integral 754

Source: 2011 Okayama University entrance exam

September 13, 2011
calculusintegrationgeometrylimitcalculus computations

Problem Statement

Let SnS_n be the area of the figure enclosed by a curve y=x2(1−x)n (0≤x≤1)y=x^2(1-x)^n\ (0\leq x\leq 1)　and the xx-axis. Find lim⁡n→∞∑k=1nSk.\lim_{n\to\infty} \sum_{k=1}^n S_k.
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