1+2+3+4... = -1/12

[stargroup100]

Originally Posted by nickcool9999

There's probably some stupid math algorithm to justify your answer but the fact of the matter is that infinite numbers summed does not produce a negative rational fraction, unless that is you're trying to be completely incorrect...

Wherever it is that you learned that OP, just ignore it. You're making math harder to justify than it needs to be. -.-

I may have fudged the terminology in the opening post for whatever reason but I assure you, I am no stranger to math.

Obviously, for any finite number of terms, the sum of the integers starting from 1 can't possibly be fractional or negative. However, we're talking about an infinite series here, which characteristically makes the problem different.

The reason why this result can even make sense is because we're talking about different contexts. Mathematical structures in different domains have different properties. When you have problems in which multiple answers can be justified, the conditions for the problem must be explained to obtain a particular solution. While in the sense of a divergent series this goes to infinity, through analytic continuation this statement can be justified. The result is actually used in quantum mechanics, and without it we wouldn't have the level of digital communication we have today.

Just because you don't like the idea doesn't make it false. And whether or not pure mathematics is difficult to justify is irrelevant. Fermat's Last Theorem was notoriously hard to justify, but people spent hundreds of years to do it, and it's an important result.

Originally Posted by nickcool9999

Mathematical Justification or Critical Thinking (Why this board exists):

ƒ(n,s)=1/n^s where (s=-1),
sub as ƒ(n,-1)=1/n^-1
ƒ(n,-1)=1/(1/n)
ƒ(n,-1)=n

Therefore, if (ƒ(n,-1)=-1/12) and ƒ(n,-1)=n, then n=-1/12. So your math is wrong anyways.

ƒ(-1/12,-1)=-1/12
ƒ(ΣI,-1)≠-1/12
∴ΣI≠-1/12

:P

wtf is this

making an assumption with no basis: "Therefore, if (ƒ(n,-1)=-1/12)"
jumping to conclusions: "n=-1/12. So your math is wrong anyways."
another assumption: "ƒ(ΣI,-1)≠-1/12"

clearly math is not your strong suit