question_answer

If \[{{S}_{1}}=\sum{n},\,{{S}_{2}}=\sum{{{n}^{2}},{{S}_{3}}=}\sum{{{n}^{3}},}\], then the value of \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{S}_{1}}\left( 1+\frac{{{S}_{3}}}{8} \right)}{S_{2}^{2}}\] equal to

A)  \[\frac{3}{32}\]            

B)  \[\frac{3}{64}\]

C)  \[\frac{9}{32}\]            

D)  \[\frac{9}{64}\]