1.

Let \[\omega \] is an imaginary cube roots of unity then the value of\[2(\omega +1)({{\omega }^{2}}+1)+3(2\omega +1)(2{{\omega }^{2}}+1)+.....\]\[+(n+1)(n\omega +1)(n{{\omega }^{2}}+1)\]  is [Orissa JEE 2002]

A. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}+n\]
B. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]
C. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}-n\]
D. None of these
Answer» B. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]


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