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I've been at this for MANY hours and I think it's time I sought help.

Question: Given $k = \frac{2 \pi}{Na}\left ( p-\frac{N}{2} \right )$, prove that $\sum_{k=1}^{N}e^{ika\left ( n-m \right )}=N\delta_{mn}$

Hint: $\sum_{p=1}^{N}=\frac{x\left ( x^{N}-1 \right )}{x-1}$ for x $\in \mathbb{C}$ and $x \neq 1$

Any help is appreciated.

Thanks in advance.

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  • $\begingroup$ The hint is not written down properly, what should it say? And also, what is $\delta_{mn}$? Actually, can you explain all symbols involved? What are they? Random numbers? Do they satisfy something? $\endgroup$
    – Mathematician 42
    Commented Nov 9, 2016 at 14:32
  • $\begingroup$ The symbol in your reply is a kronecker delta. m,n and N are all natural numbers. a is some constant. $\endgroup$
    – Mathematicing
    Commented Nov 9, 2016 at 14:33
  • $\begingroup$ I think we can prove it with exponential Fourier-series relations , and Fourier analysis I hope it can help you $\endgroup$
    – W.R.P.S
    Commented Dec 17, 2016 at 20:31

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