# Can anyone tell the proof of 1+2+3+4+5+6+7+8+........upto infinity= -1/12 ?

Noone can proove this thesis, because it is false.

The left side of the expression is a sum of an infinite sequence. Only geometrical sequence can have finite sum of all terms, but this sequence is not a geometrical one therfore it is not convergent (i.e. does not have finite sum).

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Here's a "proof" from Srinivasa Ramanujan...

The most straightforward non-rigorous "proof" is credited to Srinivasa Ramanujan and goes something like this:

After subtracting, we obtain:

Now:

Keep in mind that manipulating divergent infinite series in this manner is not really valid.

Ramanujan developed techniques that are used in quantum field theories to formally assign finite values to divergent infinite sums.

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The statement that (1 + 2 + 3 + 4 + \ldots) sums to (-\frac{1}{12}) is not correct. The series (1 + 2 + 3 + 4 + \ldots) diverges to positive infinity. However, in certain contexts like string theory and analytic continuation, this divergent series can be assigned a value of (-\frac{1}{12}) for specific purposes, but it's crucial to understand that this is not the same as saying the sum converges to (-\frac{1}{12}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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