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Interesting Results and Queries

The following have been known and proven many times on this website. The following results are to do with convergent/divergent series summation, the proofs of which I can post, or can be found on the website

Equation 1:

\(1 + 1 - 1 + 1 - 1 + 1\ldots = \frac12\)

Equation 2:

\(1 - 2 + 3 - 4 + 5 - 6\ldots = \frac14\)

Equation 3:

\(1 + 2 + 3 + 4 + 5 + 6\ldots= \frac{-1}{12}\)

My question is,

Is \(1 + 1 + 1 + 1 + 1 + 1\ldots = 0\)?

Here is my logic, please feel free to correct me and point out mistakes

\(s = 1 + 2 + 3 + 4 + 5 + 6\ldots= \frac{-1}{12}\)

So,

\( s - s = (1 + 2 + 3 + 4 + 5 + 6...) + (- 1 - 2 - 3 - 4 - 5...) = 1 + 1 + 1 + 1 + 1 + 1 = 0\)

Please reply to this and comment on my logic and whether or not I am mistaken

Thank You

Note by Nanayaranaraknas Vahdam
2 years, 11 months ago

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