计算1/x(x+1)+1/(x+1)(x+2)…+1/(x+1998)(x+1999)

题目

计算1/x(x+1)+1/(x+1)(x+2)…+1/(x+1998)(x+1999)

答案

这到题得用到一个公式1/x(x+1)=1/x-1/(x+1)
所以原式等于1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+1998)-1/(x+1999)
正,负向抵消得1/x-1/(x+1999)
原式=1/x-1/(x+1999)