- #1

- 854

- 13

## Homework Statement

The number of times the function [itex] \sum_1^{2009} \dfrac{r}{x-r} [/itex] vanishes is

## Homework Equations

## The Attempt at a Solution

Expanding the sum and writing first few terms of it

[itex]\frac{1}{x-1} + \frac{2}{x-2} + \frac{3}{x-3} ... [/itex]

Now if I take the LCM I will get a polynomial of degree 2008 in the numerator and (x-1)(x-2)...(x-2009) in the denominator. f(x) vanishes when the num becomes 0. In other words I have to find roots of the num. But how can I be sure that all its 2008 roots will be real?