Find the sum to $n$ terms of the following series: $$\dfrac {2}{5}+\dfrac {6}{5^2}+\dfrac {10}{5^3}+\dfrac {14}{5^4}+………$$
My Attempt: Let $$S_n=\dfrac {2}{5} + \dfrac {6}{5^2}+\dfrac {10}{5^3}+\dfrac {14}{5^4}+……+\dfrac {4n-6}{5^{n-1}}+\dfrac {4n-2}{5^n}$$ Also, $$\dfrac {1}{5} S_n=\dfrac {2}{5^2}+\dfrac {6}{5^3}+\dfrac {10}{5^4}+\dfrac {14}{5^5}+……+\dfrac {4n-6}{5^n}+\dfrac {4n-2}{5^{n+1}}$$
How do I solve further?
Isn't there any general method to solve such problems?