作业帮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：2024/05/06 14:44:34
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