奥数之家
奥数论坛
简短留言
| 首页 | 竞赛大纲 | 优秀前辈 | 视频提示 | 专题讲座 | 论文锦集 | 综合训练 | 修身养性 | 家教平台 | 奥数论坛 |
 
The 7th Balkan Mathematical Olympiad
1990年第7届巴尔干地区数学奥林匹克
  1. The sequence un is defined by u1 = 1, u2 = 3, un = (n+1) un-1 - n un-2. Which members of the sequence which are divisible by 11 ?
  2. Expand (x + 2x2 + 3x3 + ... + nxn)2 and add the coefficients of xn+1 through x2n. Show that the result is n(n+1)(5n2 + 5n + 2)/24.
  3. The feet of the altitudes of the triangle ABC are D, E, F. The incircle of DEF meets its sides at G, H, I. Prove that ABC and GHI have the same Euler line (the line through the circumcenter and the centroid).
  4. The function f is defined on the positive integers and f(m) ≠ f(n) if m - n is prime. What is the smallest possible size of the image of f.
点击此处查看相关视频讲解
在方框内输入单词或词组
建议使用:IE 6.0及以上版本浏览器。不支持 Netscape浏览器。 本站空间由北京师范大学提供
Copyright © 2005-2007 aoshoo.com All Rights Reserved 滇ICP备05000048号
MSN:shuxvecheng@hotmail.com QQ:316180036 E-mail:aoshoo@sina.com 电话:15810289082