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









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