Originally posted by JeffW:
[b]
Originally posted by RocketX:
[b]The total is $1.002. I don't know why he would send .002 cents (charged in fractional cents?). Maybe having to send a check for such a dumb total inspired the clever check writing.
The series E(1/2^n) from 0 to infinity adds up to 2 with infinite terms.
e^(i*pi) is -1.
So it's 0.002 + -1 + 2 = 1.002
It seems to me his would be correct if the series started with n = 0. However, since the first term is n = 1, what you end up with is:
1/2 + 1/4 + 1/8 +. . . . + 1/inf = 1
e^xi = cos(x) + sin(x)*i = -1 + 0 * i = -1
So I end up with 2/10 of a cent.[/b]