Fool's problem of the day,

Prove that $ \large \sum \limits_{r=0}^{n-1} \sin( \alpha + r \beta) = 0 $ if $ \large \beta $ is an even multiple of $ \large \frac \pi n $.

Question

Fool's problem of the day,

Prove that $ \large \sum \limits_{r=0}^{n-1} \sin( \alpha + r \beta) = 0 $ if $ \large \beta $ is an even multiple of $ \large \frac \pi n $.

lalaly · Answer

Fools problems are depressing:p

anonymous · Answer

lol you should start singing lal lala lla lala llal lallala lalala :P

lalaly · Answer

haha i am singing something elseee:P

anonymous · Answer

what is that? lol

lalaly · Answer

you know lol

anonymous · Answer

;-)

phi · Answer

β is an even multiple of π/n. i.e. B= 2pi * m/n
I think you have to put a further restriction on B, that is B≠ 2pi  (or integer m≠n)

I believe you can recast this problem as performing a discrete fourier transform on a constant, and then evaluating at F(k=1). F(k) = 0 for all k except 0.

nikvist · Answer

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