1
In this video I go over the sum of the series whose terms are reciprocals of the positive integers whose only prime factors are 2s and 3s. Recall that a prime number is a number that can only be divided cleanly by itself or 1, for example the numbers 2, 3, and 5. A prime factor is a prime number that can divide into a number cleanly, for example 3 and 2 are prime factors of the number 6. A reciprocal is a number of the form 1/x. When writing out such a series of reciprocals, I show that we can formulate it as a double summation, where one summation is for the 1/2 terms and the other summation is for the 1/3 terms. Separating these further, I show they are indeed convergent geometric series. This means we can simply apply the geometric series summation formula and finally obtain the number 3. A truly fascinating result to what at first seemed a very convoluted problem!
The timestamps of key parts of the video are listed below:
This video was taken from my earlier video listed below:
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: contact@mes.fm
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
Comments:
Reply:
To comment on this video please connect a HIVE account to your profile: Connect HIVE Account