Question

已知m=2005,求m/（1x2）+m/（2x3）+m/（3x4）...+m/（2003x2004）+m/(2004x2

Answer 1

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

=m[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2003×2004)+1/(2004×2005)]

=m(1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004+1/2004-1/2005)

=m(1-1/2005)

=2004m/2005

=2004×2005/2005

=2004