共查询到20条相似文献,搜索用时 78 毫秒
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20 0 1年全国高中数学联赛题 5为 :若 (1+x +x2 ) 10 0 0 的展开式为a0 +a1x +a2 x2 +… +a2 0 0 0·x2 0 0 0 ,则a0 +a3+a6 +a9+… +a1998的值为 ( )(A) 3333. (B) 36 6 6 .(C) 3999. (D) 32 0 0 1.该题构思巧妙 ,解法灵活 ,可谓独具匠心 .笔者经研究发现 ,此处a1+a4 +a7+… +a1999=a2 +a5+a8+… +a2 0 0 0 =3999,因此 ,此题结论可以推广 .推广 1 设 (1+x +x2 ) n(n∈N)的展开式中 ,指数能被 3整除的项的系数和为An,除以 3余 1的项的系数和为Bn,除以 3余 2的项的系数和为Cn,则An=Bn=… 相似文献
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题目 已知数列{an}满足:a1=2t-3(t∈R,且t≠1),an+1=(2tn+1-3)an+2(t-1)tn-1/an+2tn-1(n∈N*).(1)求数列{an}的通项公式;(2)若t>0,试比较an+1与an的大小. 相似文献
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2004年全国高中数学联赛吉林赛区初赛第四大题是:设ai∈R ,i=1,2…,5.求a1a2 3a3 5a4 7a5 a2a3 3a4 5a5 7a1 … a5a1 3a2 5a3 7a4的最小值.本文笔者将给出这道试题的一个推广及应用.命题设xi>0(i=1,2,…,n),n∈N,n≥3,数列{λn}成正项等差数列,则x1λ1x2 λ2x3 … λn-1xn x2λ 相似文献
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荀径 《数学的实践与认识》2016,(15):45-46
2015年全国研究生数学建模竞赛D题是面向节能的单/多列车优化决策问题,题中包括3个问题:单列车节能运行优化控制、多列车节能运行优化控制问题、列车延误后运行优化控制问题.分别对这三个问题做一些评述. 相似文献
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简述2016年全国研究生数学建模竞赛D题军事行动避空侦察的时机和路线选择的命题背景、数据来源和设计思路,并对参赛论文所涉及的有关问题进行评注. 相似文献
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给出了一个积分型Cauchy中值定理的推广,并讨论了连续函数的积分型Cauchy中值定理的逆问题. 相似文献
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《Optimization》2012,61(6):807-825
In this article, the author examines the properties of interior variations and indicates how to use them in order to formulate the necessary condition of optimality for problems of dynamic optimization, in particular, problems of variational calculus and of optimal control. For optimal control problems, an optimization technique based on interior variations and polynomial approximations is suggested and then illustrated by an explanatory example. 相似文献
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The inverse problem of the calculus of variations for second-order nonlinear and linear systems of differential-difference equations is considered. The relationship between the formal potentiality of a linear system with constant coefficients and the parity of its characteristic function is established. 相似文献
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Cinzia Bonotto Milena Basso 《International Journal of Mathematical Education in Science & Technology》2013,44(3):385-399
In common teaching practice the habit of connecting mathematics classroom activities with reality is still substantially delegated to wor(l)d problems. During recent decades, a growing body of empirical research has documented that the practice of word problem solving in school mathematics does not match this idea of mathematical modelling and mathematization. If we wish to construct ‘real problems arising from real experiences of the child’ following the spirit of these new suggestions, we have to make changes. On the one hand we have to replace the type of activity in which we delegate the process of creating an interplay between reality and mathematics by substituting the word problems with an activity of realistic mathematical modelling, i.e. of both real-world based and quantitatively constrained sense-making; and, on the other hand, to ask for a change in teacher beliefs; furthermore, a directed effort to change the classroom socio-math norms will be needed. This paper discusses some classroom activities that takes these factors into account. 相似文献
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Hongwei Chen Parviz Khalili 《International Journal of Mathematical Education in Science & Technology》2013,44(1):119-125
In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals. 相似文献