[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]
So, we need to find
[tex]\sum^{\infty}_{n=1} n(5/6)^n
[/tex]
Let this sum be S.
Then,
[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]
