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22题 :已知a0 ,数列 {an}满足a1 =a ,an + 1 =a+1an,n =1,2 ,… .(Ⅰ )已知数列 {an}的极限存在且大于0 ,求A =limn→∞an(将A用a表示 ) ;(Ⅱ )设bn =an-A ,n=1,2 ,… ,证明 :bn+ 1 =-bnA(bn +A) ;(Ⅲ )若|bn|≤ 12 n 对n=1,2 ,…都成立 ,求a的数值范围 .压轴题第 (Ⅰ )问、
22 questions: Given a0, the series {an} satisfies a1 =a, an + 1 =a+1an,n = 1,2,... (I) The limit of the known sequence {an} exists and is greater than 0, seeking A =limn→∞an (represent A with a); (II) Let bn =an-A,n=1,2,... prove: bn+ 1 =-bnA(bn +A) ;(III) if |bn |≤ 12 n is true for n=1,2,..., find the numerical range of a. The final question (I) asks,