Stange series!

What is the sum of this infinite series?

$1-2+3-4+5-6+7-8+...$

#NumberTheory

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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`	$\sin \theta$
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Comments

It should be a divergent obstacle series. However, it has an "answer". This sum is actually the square of $1-1+1-1+\cdots$ , which is $\dfrac{1}{4}$

Isaac YIU Math Studio - 1 year, 7 months ago

How?

Fahim Muhtamim - 1 year, 7 months ago

The infinite series $1+2x+3x^2+4x^3+\cdots=(1+x+x^2+\cdots)^2=\dfrac{1}{(1-x)^2}$ , if we substitute $x=-1$ , we get the answer

Isaac YIU Math Studio - 1 year, 7 months ago

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}`	$\boxed{123}$