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`(2^(n-1)(n-2)+1)/(2^(n)-1)``(2^(n)(n-2)+1)/(2^(n)-1)``(2^(n-1)(n-1)-1)/(2^(n)-1)`none of these

Solution :

`"From "(1),log (x^(n)-1)=log (x-1)+log(x-a_(1))+...+log(x-a_(n-1))` <br> Differentiating w.r.t. x, we get <br> `(nx^(n-1))/(x^(n)-1)=(1)/(x-1)+(1)/(x-a_(1))+(1)/(x-a_(2))+...+(1)/(x-a_(n-1))" (2)"` <br> Putting x = 2 in (2), we get <br> `(n2^(n-1))/(2^(n)-1)=1+(1)/(2-a_(1))+(1)/(2-a_(2))+...+(1)/(2-a_(n-1))` <br> `"or " (1)/(2-a_(1))+(1)/(2-a_(2))+...+(1)/(2-a_(n-1))=(n2^(n-1))/(2^(n)-1)-1` <br> `=(n2^(n-1))/(2^(n)-1)` <br> `(2^(n-1)(n-2)+1)/(2^(n)-1)`