how to derive that the IFFT when x(k) = 1 is an impulse

Hello All,

     The IDFT equation is

     x(n) = 1/N * {summation(k=0:N-1) (X(k) * exp(j*2*pi*k*n/N))}

     My question is if

     X(k) = [1 1 1 1]; example case of N=4

     Using the IDFT equation how to prove that 

     x(n) = [1 0 0 0];

Regards
Bharat

Hello All,

      I have worked out the equations and now it seems to
      work as expected.

      Please do not respond to this post.

Thanks and Regards
Bharat Pathak