用二进制解2003年(全国卷)理科压轴题

题　设 { an}是集合 { 2 t+2 s|0≤ s相似文献   

巧用等差、等比数列的基本性质解题

等差数列和等比数列具有以下基本性质:1)在等差数列{an}中,若m n=s t(m,n,s,t∈N*),则am an=as at;2)在等比数列{an}中,若m n=s t(m,n,s,t∈N*),则am·an=as·at.注这两个命题的逆命题都不正确.例如,通项为an=2的等差数列满足a1 a3=4=a5 a8,但:1 3≠5 8.在解决数列问题时,如能灵活运用性质1),2),往往能为解题带来事半功倍的效果.例1 1)在等差数列{an}中,若a3 a4 a5 a6 a7=450,则a2 a8=;2)若等差数列{an}的各项都是负数,且a32 a82 2a3·a8=9,则其前10项的和S10=;3)若{an}是各项均为正数的等比数列,且a3·a5=8,则log2a2 log2a3 log2a5 log2a…     

对一道高考题的进一步探究

20 0 3年全国高考数学试卷 (理工农医类 )的第2 2题 (Ⅰ )是这样一道题 :设 {an}是集合 { 2 t+ 2 s| 0≤s相似文献   

用对应观点解一道高考题

2003年高考全国卷理科(22)题是: (Ⅰ)设{ax}是集合{2l 2s|O≤s相似文献   

有趣的数表与数阵问题(下)

<正>例7设{an}是集合{2~t+2~s|0≤s相似文献   

对2000年一道高考试题的研究与推广

今年全国高考数学理科第 (2 0 )题为 :( )已知数列 { cn} ,其中 cn =2 n + 3n,且数列 { cn+ 1 - pcn}为等比数列 ,求常数 p:( )设 { an}、{ bn}是公比不相等的两个等比数列 ,cn =an + bn,证明数列 { cn}不是等比数列 .这是一道“主要考查等比数列的概念和基本性质 ,推理和运算能力”的好题 .从本校许多考生的信息反馈来看 ,该试题起点低 ,入手宽 ,且具有一定的难度和较好的区分度 .经研究 ,笔者发现该试题所述的两个问题可归结为同一个模型 ,从而可用统一的方法加以解决 .定理　设 a、b、c、r、s、t均为实常数 ,则等式　　　 arn-1 + b sn-1 =c tn-1 (* )对任意的 n∈ N恒成立的充要条件为　　　　 a =b=c=0 ;(1)或　　 a + b=c=0 ,r=s;(2 )或　　 a =0 ,b =c,s=t;(3)或　　 b =0 ,a =c,r=t;(4 )或　　 a + b=c,r=s=t. (5 )证明　 (充分性 )逐一验证 (1)～ (5 )知它们均可分别使 (* )对任意的 n∈ N恒成立 ,故“充...     

递推数列寻找特根(续)——从2010年全国卷Ⅰ第22(1)说起

下题由2010年全国1卷第22(1)题改编,求数列{bn}改成了求数列{an}的通项公式. 题3 已知数列{an}中,a1=1,an+1=5/2-1/an.求数列{an}的通项公式. 求根 设递推式an+1=5/2-1/an的特征方程s=5/2-1/s,解之得s1=2或s2=1/2.     

Ergodic Retraction Theorem and Weak Convergence Theorem for Reversible Semigroups of Non-Lipschitzian Mappings

Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u（.） of T, ∩s∈G ^-CO{u（t） ： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t） ： t ∈ G} to a common fixed point of T.     

THE GROWTH OF RANDOM DIRICHLET SERIES (I)

We consider random Dirichlet serieswhere an C C, 0 5 A. T co, Zn(w) is a sequence of random variables defined in the probabilityspace (fi, F, P), s = a it(a, t E R).Conveniently we consider Dirichlet seriesThe convex regularized sequence of {-- In la. l} is noted as {-- In la; I}, set a.(w) = a.Zn(w),the convex regularized sequence of {-- In la.(w)l} is noted as {-- In la;(w) l} where a.(a.(w)) isthe abscissa of convergence about f(s)(f(s, w)).Lemma 1 (i) If Z.(w) satisfiesthen a.s.…     

ON DISCRETE PHENOMENA IN THE MIXED PROBLEM

On discrete phenomena in uniqueness of the initial value problem, F. Treves studied an interesting example and proved that the Oauohy problem \[\left\{ \begin{array}{l} {L_p}u = {u_{xx}} - {x^2}{u_{tt}} + p{u_t} = 0,t \ge 0;\u(x,0) = {u_t}(x,0) = 0, \end{array} \right.\] has non-triyial solutions if and only if p = 3, 5, …. Wang Guang-ymg and others proved that the Oauohy problem \[\left\{ \begin{array}{l} {L_p}u = 0,t \ge 0;\u(x,0) = {\varphi _1}(x);{u_t}(x,0) = {\varphi _2}(x), \end{array} \right.\] and Goursat problem \[\left\{ \begin{array}{l} {L_p}u = 0,t \ge \frac{{{x^2}}}{2};\u(x,\frac{{{x^2}}}{2}) = {\varphi _3}(x), \end{array} \right.\] both have a unique solution if and only if p≠1, 3, 5, …. In this paper, we discuss in detail the equation Lvu = 0 for discrete phenomena. We prove that solution of the mixed problem \[\left\{ \begin{array}{l} {L_p}u = 0,x \ge 0,t \ge 0,\u(x,0) = \varphi (x),\{u_t}(x,0) = \psi (x),\u(0,t) = 0 \end{array} \right.\] is not only existent but also unique, for р≠3, 7, 11，…，neither existence nor uniqueness could be proved in this problem, for p = 3, 7, 11，….，more precisely, only under some compatibility condition can the solution exist for the equation \({L_p}u = 0\).