Please prove or disapprove this equality

[bayes]

Please help me prove or disapprove the following equality:

sum_(n in Z)e^(2 pi i n s) = 2 delta (s)

Z is the set of integers and s any variable and delta is the usual delta function that is 0 when s is different from 0 and infinite if s is 0.

Thanks

 

[uart]

I think it's false.

Based on Fourier series I think the RHS of that equality should, [instead of 2 delta(s)], read:

$$\sum_{n\,\, \mbox{\rm in Z}} \delta(s-n)$$

Hint : Consider the Fourier series expansion of the above (period=1) function of s.

 

[Wizlem]

By what you wrote above did you mean

$$\sum^{\infty}_{n=-\infty} e^{2 \pi i n s}$$

This sum doesn't converge because $$lim_{n\rightarrow\infty}e^{2 \pi i n s}\neq0$$