1a21b2?a2?ab1a1111．设abcd?1，证明：
b2b?0. c2?1c2c1c1d2?1d2d1d1
a1?b1xa1x?b1c1a1b1c12．a2?b2xa2x?b2c22?(1?x)a2b2c2. a3?b3xa3x?b3c3a3b3c3
11113．abcda2b2c2d2?(b?a)(c?a)(d?a)(c?b)(d?b)(d?c)(a?b?c?d). a4b4c4d4
11?1a1a2?an4．
a21a22?a2nn????ai(aj?ai).
i?11??i?j?nan?21an?2?an?22nan1an2?ann
1115．设a,b,c两两不等，证明abc?0的充要条件是a?b?c?0. a3b3c3
参考答案
一．单项选择题
A D A C C D A B C D B B 二．填空题
1.n; 2.“?”; 3.a14a22a31a43; 4.0; 5.0; 6.(?1)n?1n!; 7.
(?1)n(n?1)2a1na2(n?1)?an1; 8.?3M; 9.?160; 10.x4; 11.(??n)?n?1; 12.?2;
n113.0; 14.0; 15.12,?9; 16.n!(1??); 17.k??2,3; 18.k?7
k?1k三．计算题
1．?(a?b?c?d)(b?a)(c?a)(d?a)(c?b)(d?b)(d?c)； 2. ?2(x3?y3)； 3. x??2,0,1; ?nn5.
(ak?1)(1?1); k?0?k?0ak?1 n7. (?1)n?(bk?ak); k?1n9. 1??xk; k?111. (1?a)(1?a2?a4). 四. 证明题 (略)
n?1 4.
?(x?ak)
k?1 6. ?(2?b)(1?b)?((n?2)?b); nn 8. (x??ak)?(x?ak);
k?1k?1 10. n?1;