Solution:

$X(k)=\sum_{n=0}^{N-1} x(n) e^{\frac{-j 2 \pi k n}{N}}\\ $

The DFT of the sequence $x(n)=\left\{\begin{array}{l}1 \text { for } 0 \leq n \leq 2 \\ 0 \text { otherwise }\end{array}\right.$

Here $x(0)=1, x(1)=1, x(2)=1, x(3)=0 ; \quad N=4$.

For k=0:

$ \begin{aligned} & X(0)=\sum_{n=0}^3 x(n)=x(0)+x(1)+x(2)+x(3) \\\\ & =3 \\\\ …