Thread: Complex Formula Proof

Suppose q = e^[(2*pi*i)/n]

Show that:

1 + 2*q + 3*q^2 + ... + n*q^(n-1) = n/(q-1)

After testing with various n I have found that this is true, however I am having trouble with the general proof.

Thanks!

Originally Posted by KatyCar

Suppose q = e^[(2*pi*i)/n]

Show that:

1 + 2*q + 3*q^2 + ... + n*q^(n-1) = n/(q-1)

After testing with various n I have found that this is true, however I am having trouble with the general proof.

Thanks!

is a geometric series. The sum is well known. Differentiate both sides.

You could also note that to get a similar result to the "geometric series". Of course, it is recognizing that you can differentiate term by term that is the crucial step.