3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links
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)).
#math #calculus #series #desmos #education
Timestamps
Solution: Graphing curves of y = x^n with Desmos graphing calculator: https://www.desmos.com/calculator/ml00mwrvpi – 0:33
Area between successive curves of x^n – 2:44
Difference in areas as an integral – 6:30
Difference is equal to the formula in the series from Example 6 – 9:03
Sum of series of differences equals one or the unit square – 9:38
