Prove me wrong

It's not porn, it's gore.

But the series diverges

>>8920889
Prove you right first

It's a sum of positive numbers, so the result, if it exists, must be positive.
Thus it can't be -1/12

>>8920889
Logic.


Next.

>>8920889
It diverges...

And it isnt even a cauchy series so it simply can not converge.

File: rps20170519_110039.jpg (5KB, 400x160px) Image search: [Google]

5KB, 400x160px

>>8920889
There i proved you wrong

This was never the famous result.

>>8920889
F[0]=1
F[n]=n
F[oo]=oo!=-1/12

>>8922016
I'm stupid that was wrong, kek
F[0]=1
F[n]=F[n-1]+n
F[n]=(n+n2)/2+1
F[oo]=(oo+oo2)+1€oo

>>8922025
F[oo]=(oo+oo2)/2+1€oo
what is my bot doing

Suppose [math] s_N=\sum_{n=1}^Nn\to-\frac{1}{12} [/math]. Then [math] s_N,s_{N-1}\to-\frac{1}{12} [/math], and [math] s_{N}-s_{N-1}=N\to 0\,; [/math] a contradiction.

File: 99.9%.gif (3MB, 384x288px) Image search: [Google]

3MB, 384x288px

>>8920889
Burden of Proof is on you.

>>8922025
well fooooooooooooooooo to you too

Fuck off erryone knows this shit is a divergent series
Come on
Come the fucking on

>>8922197
t. brainlet who doesn't know what analytic continuation is

Diverges by integral test.

>>8920889
I don't know man, that picture sure does get me hard.

>>8921232
Not OP but here's some fun:

A = 1 -1 +1 -1 ...
1 - A = 1 -(1 - 1 + 1...) = A
1 = 2A
A = 1/2

----

B = 1 - 2 + 3 - 4...
B + B = 1 + (1 - 2) + (-2 + 3) + (3 - 4)...
B + B = 1 - 1 + 1 - 1... = A
2B = 1/2
B = 1/4

----

S = 1 + 2 + 3 + 4 + 5...
S - B = (1-1) + (2 - (-2)) + (3-3) + (4 - (-4)) ...
S - B = 0 + 4 + 0 + 8 + 0 + 12....
S - B = 4(1+2+3+4...)
S - B = 4S
-B = 3S
-1/12 = S

>>8922613
Then stop abusing the notation of equality. The sum of all natural numbers is not "equal" to -1/12 in the usual sense. They are in a different equivalence relation.

>>8925722
but then you can't add up divergent series in the classical sense this picture and your representations suggest. This doesnt mean its wrong since this is the representation zeta(-1) but its not like this makes any sense in regard to sums.

it's a false statement

zeta(-1) = -1/12

but thats cause of analytic continuation and has nothing to do with that sum

>>8925776
>but thats cause of analytic continuation and has nothing to do with that sum

Bingo

It's important to understand that just because two functions yield the same results on a certain range then they're automatically the same function.

For example, the geometric series on x yields the same result as 1/(1-x) if |x| < 1, but in no way does that imply that the geometric series function and the 1/(1-x) function are the same function.

>>8925722
a=0
b=negative infinite
s=positive infinite

>>8925853
a=0|1
b=+-inf
s=inf

>>8925853
also as recursive function with recurrence equation solution:
a[n]=Ca+((-1)^n - 1)/2
b[n]=Cb+((-1)^n (2 n + 1) - 1)/4
s[n]=Cs+n (n + 1)/2