已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman
问题描述：
已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman
答
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