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

#ShockingResults #SummationOfSeries #Queries

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$