1/1*2+1/2*3+1/3*4+…+1/49*50

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/03 09:40:08
1/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…+1/49*501/1*2+1/2*3+1/3*4+…

1/1*2+1/2*3+1/3*4+…+1/49*50
1/1*2+1/2*3+1/3*4+…+1/49*50

1/1*2+1/2*3+1/3*4+…+1/49*50
1/1*2+1/2*3+1/3*4+…+1/49*50
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/49-1/50)
=1-1/2+1/2-1/3+1/3-.+1/49-1/50
=1-1/50
=49/50