数列满足An+1=An/(3-2An).A1=1/4,求An通项公式.左边的1是小1.
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![数列满足An+1=An/(3-2An).A1=1/4,求An通项公式.左边的1是小1.](/uploads/image/z/3172138-34-8.jpg?t=%E6%95%B0%E5%88%97%E6%BB%A1%E8%B6%B3An%2B1%3DAn%2F%283-2An%29.A1%3D1%2F4%2C%E6%B1%82An%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F.%E5%B7%A6%E8%BE%B9%E7%9A%841%E6%98%AF%E5%B0%8F1.)
数列满足An+1=An/(3-2An).A1=1/4,求An通项公式.左边的1是小1.
数列满足An+1=An/(3-2An).A1=1/4,求An通项公式.左边的1是小1.
数列满足An+1=An/(3-2An).A1=1/4,求An通项公式.左边的1是小1.
An+1(3-2An)=An
=>
-2An+1An + 3An+1 - An = 0
=>
-2 + 3/An - 1/An+1 = 0
=>
(1/An+1 - 1) = 3(1/An - 1)
=>
1/An - 1 = 3^(n-1)*(1/A1 - 1) = 3^n
=>
An = 1/(3^n + 1)
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