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]

Question

TuteeHUB · Accepted Answer

$${{\left[ \frac{n(n+1)}{2} \right]}^{2}}$$

TuteeHUB · Answer

$${{\left[ \frac{n(n+1)}{2} \right]}^{2}}+n$$

TuteeHUB · Answer

$${{\left[ \frac{n(n+1)}{2} \right]}^{2}}-n$$

TuteeHUB · Answer

None of these

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. \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]

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]

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