Through the Living Wrath
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Guys I have a mindbender for you! (Daily AI impersonation: check)
Stop me, if you’ve heard this one before. (Daily Jinu impersonation: check)
Its not something I came up with, I’m not nearly smart enough
If C = 1 + 2 + 3 + 4 + 5 …C is -1/12
The sum of all positive integers is -1/12
Proof:SpoilerS = 1 - 1 + 1 - 1 + 1 … to infinity
S - 1 = - 1 + 1 - 1 + 1 … to infinity
S - 1 = -S
2S = 1
S = 1/2
Z = 1 - 2 + 3 - 4 + 5 … to infinity
Splitting each number into a sum of ones…
Z = 1 - 1 + 1 - 1 + 1 … (This line = S
- 1 + 1 - 1 + 1 … (This line = -S)
+ 1 - 1 + 1 … (This line = S)
- 1 + 1 … (This line = -S)
…
So
Z = S - S + S - S + S …
Factor out the S…
Z = S(1 - 1 + 1 - 1 + 1 …)
Z = S(S) [YES IT IS THE SECRET SERVICE]
Z = (1/2)(1/2) = 1/4
C = 1 + 2 + 3 + 4 + 5 …
C - Z = 1 + 2 + 3 + 4 + 5 …
- 1 + 2 - 3 + 4 - 5 …
= 0 + 4 + 0 + 8 + 0
C - Z = 4 + 8 + 12 + 16 …
C - Z = 4(1 + 2 + 3 + 4 + 5)
C - Z = 4C
3C = -Z
C = -Z/3
C = -1/12
