Published: 24 Jul 2026 › Updated: 24 Jul 2026
Exercise 1: Sum of differences between curves y = x^n as an infinite series
In this video, I show that the sum of differences between successive positive integer powers x^n for 0 ≤ x ≤ 1 can be written as an infinite series, and the resulting sum is equal to 1 or the unit square. This is the same series as in Example 6, thus this provides a geometric interpretation of the series 1/(n(n+1)).
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