### How to tell that you've ticked off an engineer

(Click on the image to enlarge.)

The check is written for an amount of 0.002 +

*e*

^{iπ}+ Σ 1/2

^{n}, as n goes from 1 to ∞.

How much is that?

Well,

*e*

^{iπ}= -1. (See here and here.)

The sum of 1/2

^{n}as n goes from 1 to infinity is equal to 1. That is:

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... + 1/∞ = 1

So, the amount of the check is 0.002 + -1 + 1 = 0.002 dollars. That's two-tenths of a cent.

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