已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman

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已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman
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已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman
已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman

已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman
2An=An-1 + An-2
2(An - An-1)=-(An-1 - An-2)
An - An-1=(-1/2)^(n-2)
An=(-1/2)^(n-2)+(-1/2)^(n-3)+……+(-1/2)^0=(2/3)*(1-(-1/2)^(n-1))
limAn=2/3