nan+1(an+1为下角标)+(n+1)an=n(n+1),a1=1,求an.,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 17:07:29
nan+1(an+1为下角标)+(n+1)an=n(n+1),a1=1,求an.,

nan+1(an+1为下角标)+(n+1)an=n(n+1),a1=1,求an.,
nan+1(an+1为下角标)+(n+1)an=n(n+1),a1=1,求an.,

nan+1(an+1为下角标)+(n+1)an=n(n+1),a1=1,求an.,
两边除以n(n+1)
a(n+1)/(n+1)=-an/n+1
两边减去1/2
a(n+1)/(n+1)-1/2=-an/n+1/2
a(n+1)/(n+1)-1/2=-(an/n-1/2)
所以an/n-1/2是等比,q=-1
所以an/n-1/2=(a1/1-1/2)*(-1)^(n-1)=1/2*(-1)^(n-1)
an=n[1/2+1/2**(-1)^(n-1)]