数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
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数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
An+1=An(1—An+1)
所以An-An+1=AnAn+1
两边同除以AnAn+1
则1/An+1-1/An=1
所以数列{1/An}是首项为1,公差是1的等差数列
所以1/An=n
即An=1/n
则Bn=1/[n(n+1)]=1/n-1/(n+1)
所以Bn的前10项的和=1-1/2+1/2-1/3+1/3-1/4……+1/10-1/11=1-1/11=10/11
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