Question

2005×（1×2/1+2×3/1+3×4/1+···+2003×2004/1+2004×2005/1）=?

Answer 1

2005×（1×2/1+2×3/1+3×4/1+···+2003×2004/1+2004×2005/1）

=2005×[(1-2/1)1+(2/1-3/1)+(3/1-4/1)+···+(2003/1-2004/1)+(2004/1-2005/1）]

=2005×(1-2005/1)

=2005×(2005/2004)

=2004