Question : Using the Ratio Test for the convergence of an infinite series, examine the convergence of the series

$\displaystyle \frac{1}{2} + \frac{1}{2.2^2}+\frac{1}{3.2^3}+ \frac{1}{4.2^4}+...$

Solution

My work::::::::::::

$\displaystyle u_n$ = $\displaystyle \sum_{n=1}^{ \infty} \ \frac{1}{n.2^n}$.............Is this correct?????