Subject : Signals & Systems

Topic :Fourier Series.

Difficulty: Medium

Given: x[n] = (1/3)^n u[n]

h[n] = (1/2)^n u[n]

Therefore, y[n] = x[n]*h[n] ------------ 1

y[n] = ∑_(k= -∞)^∞〖x[k] h[n-k]〗 -------------- 2

Using the formula, ∑_(k= 0)^N〖 a^k= (1-a^(N+1))/(1-a) 〗

y[n] = (1/2)^n (1-(2/3)^(n+1))/(1- 2/3)

∴y[n] =〖3(1/2)〗^n [1- (2/3)^(n+1)]