Find the sum of the n terms of the series $2\cdot2^0+3\cdot2^1+4\cdot2^2+\dots$ Find the sum of the n terms of the series: 

$2\cdot2^0+3\cdot2^1+4\cdot2^2+\dots$

I don't know how to proceed. Please explain the process and comment on technique to solve questions of similar type. 
Source: Barnard and Child Higher Algebra. 
Thanks in Advance!

This lookslike a double sum. Try rewriting it the following way.
$$2\cdot 2^0+3\cdot 2^1+4\cdot 2^2+...+(n+2)\cdot 2^n =$$
$$=2\cdot 2^0+2\cdot 2^1+2\cdot 2^2+...+2\cdot 2^n$$
$$+1\cdot2^1+1\cdot 2^2+...+1\cdot 2^n$$
$$+1\cdot 2^2+...+1\cdot 2^n$$
$$ \cdots $$
The Terms are now a simple geometric series.
