Question 9.6: z transform using the accumulation property Using the accumu......

First express n u[n] as an accumulation

n\,\mathbf{u}[n]=\sum_{m=0}^{n}\mathbf{u}[m-1].

Then, using the time-shifting property, find the z transform of {{u}}[n-1],

{u}[n-1]\overset{\mathcal Z}{\longleftrightarrow } z^{-1}{\frac{z}{z-1}}={\frac{1}{z-1}},\ \left|z\right|\gt 1.

Then, applying the accumulation property,

n\mathbf{u}[n]=\sum_{m=0}^{n}\operatorname{u}[m-1]\overset{\mathcal Z}{\longleftrightarrow }\left\lgroup{\frac{z}{z-1}}\right\rgroup {\frac{1}{z-1}}={\frac{z}{(z-1)^{2}}},~|z|\gt 1.