help! how do u find this sum of series: summation of n=1 to infinity ((2^(n+1))-(3^(n-1)))/(5^n), would you plz include steps too? thank you?

Sol
Σ(n=1 to ∞)_[2^(n+1)－3^(n－1)]/5^n
=Σ(n=1 to ∞)_2^(n+1)/5^n－Σ(n=1 to ∞)_3^(n－1)/5^n
=2*Σ(n=1 to ∞)_2^n/5^n－(1/3)*Σ(n=1 to ∞)_3^n/5^n
=2*Σ(n=1 to ∞)_(2/5)^n－(1/3)*Σ(n=1 to ∞)_(3/5)^n
=2*(2/5)/(1－2/5)－(1/3)*(3/5)/(1－3/5)
=2*(2/3)－(1/3)*(3/2)
=4/3－1/2
=5/6