Discrete Fourier series derivation

[kidsasd987]

Hello,

*please refer to the table above.

I started from x(n)=x(n*Ts)=x(t)*delta(t-nTs),

how can we have finite terms for discrete time F.S

can anyone provide me a derivation or proof for Discrete F.S.?

 

[Dr. Courtney]

Think about how you would numerically integrate with the rectangle method. What would the sum look like?