1/1×2+1/2×3+1/3×4+1/4×5+1/5×6……+1/2002×2003+1/2003×2004

题目

1/1×2+1/2×3+1/3×4+1/4×5+1/5×6……+1/2002×2003+1/2003×2004
用简便算法解这道题.

答案

1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2002×2003)+1/(2003×2004)
=1-1/2+1/2-1/3+1/3-1/4.-1/2003+1/2003-1/2004
=1-1/2004
=2003/2004
利用公式 1/n(n+1) = 1/n -1/(n+1)