Question

What does this e term equal to just i, and imaginary number?

Answer 1

\[\sum_{k=\infty}^{\infty} {e}^{-i 6\pi (k-(\frac{ 1 }{ 12 }))}\]

Answer 2

the term inside the summation is equal to i for some reason

Answer 3

Every term except the one at k=zero has a corresponding term with opposite sign that cancels it. That means the summation is just the one term, which is exp(i pi/2)=i.

Answer 4

Oh right that make senses thanks so much for your help!