summation - Question on a tricky Arithmo-Geometric Progression::

$$\dfrac{1}{4}+\dfrac{2}{8}+\dfrac{3}{16}+\dfrac{4}{32}+\dfrac{5}{64}+\cdots\infty$$

This summation was irritating me from the start,I don't know how to attempt this ,tried unsuccessful attempts though.

Answer

$$\begin{align}
S&=\qquad \frac 14+\frac 28+\frac 3{16}+\frac 4{32}+\frac 5{64}+\cdots\tag{1}\\
2S&=\frac 12+\frac 24+\frac 38+\frac 4{16}+\frac 5{32}\cdots\tag{2}\\

(2)-(1):\qquad\\
S&=\frac 12+\frac 14+\frac 18+\frac 1{16}+\frac 1{32}\cdots\\
&=\frac {\frac 12}{1-\frac 12}\\
&=\color{red}1
\end{align}$$