一道初二奥数竞赛题
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+99)(x+100)
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+…… +[1/(x+99)-1/(x+100)]
=1/x-1/(x+100)
=100/x(x+100)
初中数学竞赛一题
549
- 495
= 54
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+99)(x+100)
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+…… +[1/(x+99)-1/(x+100)]
=1/x-1/(x+100)
=100/x(x+100)
549
- 495
= 54