1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 15:41:37
![1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=](/uploads/image/z/2737208-56-8.jpg?t=1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%2B1%2F5%2A6%2B1%2F6%2A7%2B1%2F7%2A8%2B1%2F8%2A9%2B1%2F9%2A10%2B.%2B1%2F96%2A97%2B1%2F97%2A98%3D)
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98
=1-½+½-1/3+1/3-¼+¼-1/5+···+1/97-1/98
=1-1/98
=97/98
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+。。。。+1/96*97+1/97*98 =1/2-1/3+1/3-1/4+……+1/97-1/98
=1/2-1/98
=24/49