Seeing Double

More proof (if any were needed) that 2 equals 1:

s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + 1/7 – 1/8 + 1/9 – 1/10 + 1/11 – 1/12 …

2s = 2 – 2/2 + 2/3 – 2/4 + 2/5 – 2/6 + 2/7 – 2/8 + 2/9 – 2/10 + 2/11 – 2/12 …

Rearrange terms:

2s = (2 – 2/2) – (2/4) + (2/3 – 2/6) – (2/8) + (2/5 – 2/10) – (2/12) …

2s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 …

But that’s just s again. So 2s = s, and therefore 2 = 1.

(Thanks, Gonzalo!)