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http://www.runningahead.com/forums/topic/a4c5268206114ea39c33433c16c522adHmmm... I'll take up the challenge, and try to figure it out.
The infinite sum is fairly easy, 1/2 + 1/4 + 1/8 + 1/16... clearly converges towards 1.
For the exp(i * pi) part, I had to look up the definition of the exponential function, since I don't do complex math that often. From Wikipedia: exp(a+bi) = exp(a) * (cos b + i sin b), so here we have:
exp(0 + pi * i)
= exp(0) * (cos pi + i sin pi)
= 1 * (-1 + i * 0)
= 1 * (-1)
= -1
So it seems the entire check is for US$ 0.002 (0.2 cents) - assuming I didn't commit some mistake in the calculation.
Difference in opinions hath cost many millions of lives: for instance, whether flesh be bread, or bread be flesh; whether whistling be a vice or a virtue; whether it be better to kiss a post, or throw it into the fire... (from Gulliver's Travels)
