question_answer

The sum of the series \[{{1}^{2}}.2+{{2}^{2}}.3+{{3}^{2}}.4+.....\] to n terms is

A)  \[\frac{{{n}^{3}}\,{{(n+1)}^{3}}+(n+3)}{6}\]         

B)  \[\frac{n\,(n+1)\,\,(3{{n}^{2}}+7n+2)}{12}\]

C)  \[\frac{n\,(n+1)}{6}\,\,[n\,(n+1)+(2n+1)]\]

D)  \[\frac{n\,(n+1)}{18}\,\,[6n\,(n+1)+2\,(2n+1)]\]

E)  None of these