已知数列{an}首项a1=1/2,a1+a2+……+an=n²an,求其通项an
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已知数列{an}首项a1=1/2,a1+a2+……+an=n²an,求其通项an
![已知数列{an}首项a1=1/2,a1+a2+……+an=n²an,求其通项an](/uploads/image/z/17434596-12-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E9%A6%96%E9%A1%B9a1%3D1%2F2%2Ca1%2Ba2%2B%E2%80%A6%E2%80%A6%2Ban%3Dn%26%23178%3Ban%2C%E6%B1%82%E5%85%B6%E9%80%9A%E9%A1%B9an)
an=n(n-1)/4 当n-1时,a1+···an-1=(n-1)²(an-1)
l两式相减
得
(n+1)/(n-1)=an/an-1
n>=2时
a2/a1*a3/a2·····an/an-1=3/1*4/2*5/3····n/n-2*n+1/n-1
n(n-1)/2=an/a1
接下来应该会了.
l两式相减
得
(n+1)/(n-1)=an/an-1
n>=2时
a2/a1*a3/a2·····an/an-1=3/1*4/2*5/3····n/n-2*n+1/n-1
n(n-1)/2=an/a1
接下来应该会了.
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