已知数列{An}满足A(n+1)=【2An (0
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已知数列{An}满足A(n+1)=【2An (0
已知数列{An}满足A(n+1)=【2An (0<=An<1/2) 2An-1 (1/2<=An<1)】,若A1=6/7,则A2011的值为________
已知数列{An}满足A(n+1)=【2An (0
A1=6/7
A2=2*6/7-1=5/7
A3=2*5/7-1=3/7
A4=2*3/7=6/7=A1
{An}是一个周期是3的数列
2011÷3=670.1
所以
A2011=A1=6/7
a1=6/7
因为1/2≤6/7<1
a2=2a1-1=5/7
因为1/2≤5/7<1
a3=2a2-1=3/7
因为0≤3/7<1/2
a4=2a3=6/7=a1
所以数列{An}每三个一循环
a2011=a(3×670+1)=a1
a2011=6/7
望采纳
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