question_answer

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