question_answer

If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+.......+{{C}_{n}}{{x}^{n}},\] then the value of \[{{C}_{0}}+2{{C}_{1}}+3{{C}_{2}}+.......+(n+1)\,{{C}_{n}}\], will be

A)  \[(n+2)\,{{2}^{n-1}}\]

B)  \[(n+1)\,{{2}^{n}}\]

C)  \[(n+1)\,{{2}^{n-1}}\]                        

D)  \[(n+2)\,{{2}^{n}}\]

E)  None of these