已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式
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已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式
已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式
已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式
Sn=n^2an
Sn+1=(n+1)^2an
两个式子一减得到:
an+1=(2n+1)an
所以an+1/an=2n+1
所以an/an-1=2n-1
(a2/a1)乘以(a3/a2)乘以(a4/a3).乘以(an/an-1)=(2n-1)!
都约掉之后得到an=(1/2)(2n-1)!
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