第一部分 专项同步练习

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;

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