/sci/ - Science & Math

>>15124123
>3
>2
>1
>liftoff
>based

[math]a = 1 + 1 + 1 + \cdots[/math]
[math]a + a + a \cdots = [/math]
[math](1 + 1 + 1 + 1 \cdots) + [/math]
[math]\quad \space \space ~ (1 + 1 + 1 \cdots) +[/math]
[math]\quad \quad \space \space ~ \space \space ~ (1 + 1 \cdots) + [/math]
[math] \quad \quad \quad \space \space ~ \space \space ~ \space \space ~ (1 + \cdots) + \cdots[/math]
Thus: [math] a+ a+ a + \cdots = 1 + 2 + 3 + 4\cdots [/math].
Since [math]a + a + a + \cdots = a (1 + 1 + 1 \cdots) = a^2[/math], we thus have that [math] 1 + 1 + 1 \cdots = \pm \frac{i}{\sqrt{12}}[/math].