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)).
3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links
#math #calculus #series #desmos #education
Timestamps:
- Exercise 1: Geometric interpretation of Example 6 – 0:00
- 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
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: @mes
Email me: [email protected]
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps