Question

2005/1*2+2005/2*3+2005/3*4+2005/4*5+.2005/2004*2005=多少?

Answer 1

2005/1*2+2005/2*3+2005/3*4+2005/4*5+...............2005/2004*2005

=2005(1/1*2+1/2*3+1/3*4……1/2004*2005)

=2005[(1/1-1/2)+(1/2-1/3)+(1/3-1/4)……(1/2004-1/2005)]

=2005(1-1/2005)

=2004