Awesome Roots Of Unity

Algebra Level 5

1mα+1mα2++1mαn\large{\dfrac{1}{m-\alpha}+\dfrac{1}{m-\alpha^2}+\cdots+\dfrac{1}{m-\alpha^n}}

Let P(z)=zn+11P(z)=z^{n+1}-1 have roots 1,α,α2,,αn1, \alpha, \alpha^2, \ldots, \alpha^n where α\alpha is a (n+1)th(n+1)^\text{th} root of unity and mm isn't a (n+1)th(n+1)^\text{th} root of unity.

Find the value of the expression above.

×

Problem Loading...

Note Loading...

Set Loading...