/sci/ - Science & Math » Thread #12047387

53KiB, 600x800, markiplier soyjak.jpg

View Same Google iqdb SauceNAO

?-1 23 ? ?

Anonymous Tue 25 Aug 17:23:29 2020 No.12047387 View Reply Original Report

Quoted By: >>12047391

And it was delicious!

Anonymous

View Same Google iqdb SauceNAO 1418058253197.png, 30KiB, 675x1127

Anonymous Tue 25 Aug 2020 17:24:32 No.12047391 Report

Quoted By:

>>12047387

Anonymous

Anonymous Tue 25 Aug 2020 17:29:29 No.12047407 Report

Quoted By: >>12047458 >>12047503

$\displaystyle \boxed{0 p^n-1 = (p-1)(p^{n-1}+p^{n-2}+ \dots +p+1) \\ \dfrac{p^n-1}{p-1} = \sum \limits_{j=0}^{n-1}p^j \\ \displaystyle \lim_{n \to \infty} \dfrac{p^n-1}{p-1} = \lim_{n \to \infty} \sum \limits_{j=0}^{n-1}p^j \\ \displaystyle \dfrac{0-1}{p-1} = \sum \limits_{j=0}^{\infty}p^j \implies \dfrac{1}{1-p} = \sum \limits_{j=0}^{\infty}p^j $

$\displaystyle p=0.1 \\ \dfrac{1}{1-0.1}=\frac{10}{9} = 1 + \frac{1}{9} \\ \sum_{j=0}^\infty 0.1^j= 1 + \sum_{j=1}^\infty 0.1^j \\ 9+1=9+9\sum_{j=1}^\infty 0.1^j \\ 1=9\sum_{j=1}^\infty 0.1^j = 0.999...\\ \dfrac{1}{3} = 3 \sum_{j=1}^ \infty 0.1^j = 0.333... $

Anonymous

Anonymous Tue 25 Aug 2020 17:39:46 No.12047458 Report

Quoted By:

>>12047407
nice

Anonymous

Anonymous Tue 25 Aug 2020 17:51:58 No.12047503 Report

Quoted By:

>>12047407
$ 9+1=9+9\sum_{j=1}^\infty 0.1^j \\ 1=9\sum_{j=1}^\infty 0.1^j = 0.999...\\ \dfrac{1}{3} = 3 \sum_{j=1}^ \infty 0.1^j = 0.333... $

Feels like a cool base 10 with decimals infinite generator to me. I'm not sure If i'd be more content with the limit expression however, which at least gives one the latitude to 'just jump to convergence' instead of the proposition of consuming the energy of the universe in j=1 to infinity iterations

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