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Question
Hello,

1 + 2 + 3 + 4 + ... = -1/12
Is there a different result(different from +-infinite)  for the sum by using other summation methods?
I mean like 1 + 2 + 3 + 4 + ... = 1/4
And I am asking for the serie and other divergent infinite series.
Summation method : all methods like regularization,analytic continuations,
CesÓro summation...
Do the compatible summation methods give same sum for the divergent infinite series?
If it so, how can be sure all compatible summation methods give same sum?
Or do we do our calculation only but only with one summation method we choose..
I hope  I can tell my question and sorry for my english.
Thanks

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

This is just not true, sorry. 1+2+3+.... is divergent. There are some games you can play with the Riemann zeta function and analytic continuation that could make it seem the equation you write is true, but it is not. The analytic continuation of the zeta function does not have the same form as an infinite sum.

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