1+2+3+4+・・・

This is irrational because this must increase infinitely basically.

This is like a black hole.

Srinivasa Aiyangar Ramanujan solved it.

2F=1

∴

F=1/2

∴

A=1/4

∴

S=-1/12

This is tricky in infinity because he moves the series.

You can also use the Zeta Function.

This is A=1-2+3-4+・・=1/4

This is the Abel's summability method.

This is F=1-1+1-1+・・・=1/2

∴

ζ(-1)=1+2+3+4+・・・=-1/12