1.

The value of the expression \[1.(2-\omega )(2-{{\omega }^{2}})+2.(3-\omega )(3-{{\omega }^{2}})+.......\]\[....+(n-1).(n-\omega )(n-{{\omega }^{2}}),\]where \[\omega \] is an imaginary cube root of unity, is [IIT 1996]

A. \[\frac{1}{2}(n-1)n({{n}^{2}}+3n+4)\]
B. \[\frac{1}{4}(n-1)n({{n}^{2}}+3n+4)\]
C. \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\]
D. \[\frac{1}{4}(n+1)n({{n}^{2}}+3n+4)\]
Answer» C. \[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\]


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