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《中学生数学》2002年第1月上期刊登的《骨牌覆盖问题与一类递推数列》一文中有两处“错误”. 其一、“解题后的回顾”之例题的最后结果:an=1/18(9·2n-2·3n)应更正为an=1/18(9·2n+1-2·3n+1).这可能是笔误,只须看前面的推导过程或将n=1,2代入验证,即可发现. 其二、定理如果x1、x2是an=c1an-1+c2an-2(n≥3)的特征方程x2=c1x+c2的两个根,那么(2)当x1=x2时,数列{an}的通项公式为: r; 将n=1,2代入验证,即可发现这是一个错误的结果.
There are two “mistakes” in the article “The domino coverage problem and the first type of recursive sequence” published in the “Middle School Mathematics” in the first issue of the first month of 2002. First, the final result of the example of “Review after problem solving”: an = 1/18 (9·2n-2·3n) should be corrected as an=1/18(9·2n+1-2·3n+1). This may be a clerical error, just look at the previous derivation process or will n= 1,2 into the verification, you can find. Second, the theorem if x1, x2 is an = c1an-1 + c2an-2 (n ≥ 3) of the characteristic equation x2 = c1x + c2 of the two roots, then (2) When x1=x2, the general formula of the series {an} is: r; Substituting n=1, 2 into the verification, it can be found that this is an erroneous result.