1/(2n-1)(2n+1)1/n(n+1)(n+2)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/22 20:04:34
1/(2n-1)(2n+1)1/n(n+1)(n+2)1/(2n-1)(2n+1)1/n(n+1)(n+2)1/(2n-1)(2n+1)1/n(n+1)(n+2)1/(2n-1)(2n+1)=1/(2

1/(2n-1)(2n+1)1/n(n+1)(n+2)
1/(2n-1)(2n+1)
1/n(n+1)(n+2)

1/(2n-1)(2n+1)1/n(n+1)(n+2)
1/(2n-1)(2n+1)=1/(2n-1) -1/(2n+1)
1/n(n+1)(n+2)=1/n(n+1)-1/(n+2)
这种公式叫做裂项公式
1-1/2=1/(1*2)
1/2-1/3=1/(2*3)
……
反过来就是裂项公式

1/(2n-1)(2n+1)=(1/2)X [1/(2n-1)+ 1/(2n+1)]
1/n(n+1)(n+2)=[1/n(n+2)] - [1/(n+1)(n+2)]=(1/2)X [1/n - 1/(n+2)]+ [1/(n+1)]-[1/(n+2)]=1/2n + 1/(n+1)- (3/2)X [1/(n+2)]