1/2*1/3+1/3*1/4+……+1/1999*1/2000

题目

1/2*1/3+1/3*1/4+……+1/1999*1/2000

答案

∵1/(1×2)＝1/1-1/2 1/(2×3)=1/2-1/3 1/(3×4)=1/3-1/4 .∴1/(1×2)+1/(2×3)+1/(3×4)+...+1/(1999×2000) =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/1999-1/2000) =1-1/2000 =1999/2000这需要做题多,以前做过这类题...