1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 01:36:34
![1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)](/uploads/image/z/4317444-36-4.jpg?t=1%2F%281%2A3%29%2B1%2F%282%2A4%29%2B1%2F%283%2A5%29%2B.%2B1%2F%28101%2A103%29)
1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)
1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)
1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)
1/[n*(n+2)]= [1/n - 1/(n+2)]/2
1/(1*3)+1/(2*4)+1/(3*5)+.+1/(101*103)
=[1/(1*3)+1/(3*5)+...+1/(101*103)]+[1/(2*4)+1/(4*6)+...+1/(100*102)]
=(1-1/3+1/3-1/5++.+1/101-1/103)/2 + (1/2-1/4+1/4-1/6+...+1/100-1/102)/2
=(1-1/103)/2+(1/2-1/102)/2
=51/103+25/102
1/(1*3)+1/(2*4)+1/(3*5)+……+1/(101*103)
=1/2*((1-1/3)+(1/2-1/4)+(1/3-1/5)+……+(1/101-1/103))
=1/2*((1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+……+1/101-1/103))
=1/2(1+1/2-1/103)
=257/206