1/12+1/23+1/34+1/45+^+1/199*200=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 03:00:52

1/1*2+1/2*3+1/3*4+1/4*5+^+1/199*200=?
1/1*2+1/2*3+1/3*4+1/4*5+^+1/199*200=?

1/1*2+1/2*3+1/3*4+1/4*5+^+1/199*200=?
1/(1*2)+1/(2*3)+...+1/(199*200)
=( 1- 1/2) +(1/2-1/3)+...+(1/199-1/200)
=1- 1/200
=199/200

1/1*2+1/2*3+1/3*4+1/4*5+^+1/199*200
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+^+1/199-1/200
=1-1/200
=199/200