The equation

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

The equation

x^n-1=0

, where

n>1

and

n\in\mathbb{N}

, has roots

a_1=1,a_2,\ldots,a_n

. The value of

\sum_{r=2}^{n}\frac{1}{2-a_r}

is (1)

\frac{2^{n-1}(n-2)+1}{2^n-1}

(2)

\frac{2^n(n-2)+1}{2^n-1}

(3)

\frac{2^{n-1}(n-1)-1}{2^n-1}

(4) None of the above