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The value of the expression 1.(2-omega)....

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………

Text Solution

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The correct Answer is:
`((n(n+1))/(2))^(2) - n`
Here `T_r=(r-1)(r-omega)(r-omega)^2]=(r^3-1)`
`therefore " "S_n=underset(r=1)overset(n)Sigma(r^3-1)=[(n(n+1))/2]^2-n`
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