Question

if x is a natural number the x+(x+1)+..........+(x+2006)is always divisible by

Answer 1

x+(x+1)+....+(x+2006)

=2007x+(1+2+....+2006)

=2007x+(2006)(2007)/2

=2007(x+2006/2)

=2007(x+1003)

So this expression is always divisible by 2007.