Find the z-transform of (i) x[n] = au[n] + bu[n] + cu[-n-1], |a| < b...

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Find the z-transform of (i) x[n] = au[n] + bu[n] + cu[-n-1], |a|< b <|c| (ii) x[n] = n²a"u[n] (iii) x[n] =e [cos (n)]u[n]- en [cos (n)]u[n 1] (b) 1. Find the inverse z-transform of X(z) = 1-2-1 (¹ + 2 − ¹)(1 — ²2-¹) ›_ x[n] is causal 2. Determine the inverse z-transform of X(z) = log(122), by (a) using the power series -Σ log(1x) = - H</ || < 1; (b) first differentiating X(2) and then using the derivative to recover x[n]. Find the z-transform of (i) x[n] = au[n] + bu[n] + cu[-n-1], |a|< b <|c| (ii) x[n] = n²a"u[n] (iii) x[n] =e [cos (n)]u[n]- en [cos (n)]u[n 1] (b) 1. Find the inverse z-transform of X(z) = 1-2-1 (¹ + 2 − ¹)(1 — ²2-¹) ›_ x[n] is causal 2. Determine the inverse z-transform of X(z) = log(122), by (a) using the power series -Σ log(1x) = - H</ || < 1; (b) first differentiating X(2) and then using the derivative to recover x[n].