$T(n) = 2T(n-1) +n, n \geqslant 2 , T(1) = 1$
$ T(n) = n + 2(n-1) + 2^2 (n-2) + \dots + 2^{(n-1)}(n -(n-1))$
$=n( 1 + 2 + \dots + 2^{n-1}) - (1.2 + 2.2^{2} +3.2^{3}+\dots+ (n-1).2^{n-1})$
$=n(2^n-1) -(n.2^n-2^{n+1}+2)$
$=2^{n+1}-n -2$
Correct Answer: $A$