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!
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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.
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