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| What now bitches? |
As it turns out, the amount on the check works out to about 1.002 dollars. Work it out if you don't believe me. :)
The short version is that sum(1/n^2) is a form of the geometric series that sums to 2. This can be proven by multiplying the nth partial sum by 2 -> S_n =1 +1/2 + 1/4 + 1/8 ... + 1/2^n -> 2*S_n = 2+ S_n - 1/2^n. You can then solve for S_n and take the limit as 1/n^2 -> infinity. You get S_n = 2 in the limit.
Also, exp(i*pi) = cos(pi) + i*sin(pi) = -1. So, you add up all these terms, and you get 1.002.
