1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 15:02:20
![1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=](/uploads/image/z/74367-63-7.jpg?t=1%2F%281%2A2%29%2B1%2F%282%2A3%29%2B1%2F%283%2A4%29%2B.1%2F%282007%2A2008%29%3D)
1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=
1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=
1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=
1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)
= (1/1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2007-1/2008)
= 1-1/2008 【中间的项正好正负抵消,只剩下头尾两项】
= 2007/2008