数学题在线解答1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)

题目

数学题在线解答1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)
当x=5时，求代数式的值。

答案

1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)=1/(x+1)-1/(x+100)=99/ (x+1)(x+100)x=5时原式=99/(6*105)=11/70