设数列｛an}满足a1=2,an+1=an+1/an(n=1,2,3.),证明：an>根号下（2n+1).急用
问题描述：
设数列｛an}满足a1=2,an+1=an+1/an(n=1,2,3.),证明：an>根号下（2n+1).急用
答
证明：(开方即 1/2 次方,用^表示)n=1时,A_1 = 4^(1/2) = 2 > (2*1 + 1)^(1/2) = 3^(1/2);假设n=k时,A_k > (2k + 1)^(1/2);则n=(k+1)时,A_(k+1) = A_k + 1/A_k;欲证结果,只需证（A_k + 1/A_k）^2 > (2k + 3);而（A_k ...