[Kamog]

The amount on the check is $0.002.

The second term, e^(i*pi) is equal to -1, which we can figure out by using Euler's formula e^(ix) = cos(x) + i sin(x), where cos(pi) = -1, sin(pi) = 0.

The third term, the summation, is equal to 1. Use the summation formula Sum = a / (1-r) for infinite geometric series where r = 1/2, a = 1, with the index n from 0 to infinity. Since the index starts from 1 in the expression, we need to subtract 1, so the term equals 1 / (1 - 0.5) - 1 = 1

Therefore the second and third terms in the amount cancel each other out, so the amount is only $0.002.