Find the Z transform of sequence x(n)

Find the Z transform for the unit step discrete function

Given the unit step function \(x[n]=u[n]\) deﬁned as \(x=\{1,1,1,\cdots \}\,\ \) for \(n\geq 0\,\), ﬁnd its Z transform.

Mathematica

Remove["Global`*"]; 
ZTransform[UnitStep[n],n,z]

Out[] = z/(-1+z)

Matlab

syms n 
pretty(ztrans(heaviside(n)))

 
    1 
  ----- + 1/2 
  z - 1

Find the Z transform for \(x[n]=\left ( \frac {1}{3}\right ) ^{n}u\left ( n\right ) +\left ( 0.9\right ) ^{n-3}u\left ( n\right ) \)

Mathematica

f[n_]:=((1/3)^n+(9/10)^(n-3))UnitStep[n]; 
ZTransform[f[n],n,z]

z (3/(-1+3 z)+10000/(729 (-9+10 z)))

Matlab

syms n 
pretty(ztrans( 
 ((1/3)^n+(0.9)^(n-3)) 
       *heaviside(n)))

       100           1 
  ------------- + ------- + 1729/1458 
  81 (z - 9/10)   3 z - 1