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1、课时作业53二项式定理一、选择题1(2012重庆高考)8的展开式中常数项为()A B C D1052n的展开式中只有第六项的二项式系数最大，则展开式的常数项是()A360 B180C90 D4535的展开式中各项系数的和为2，则该展开式的常数项为()A40 B20 C20 D404若二项式n的展开式中二项式系数的和是64，则展开式中的常数项为()A240 B160C160 D2405(2012安徽高考)(x22) 5的展开式的常数项是()A3 B2C2 D36如果n的展开式中二项式系数之和为128，则展开式中的系数是()A7 B7C21 D217已知(1x)5a0a1xa5x5，则a0(a2a
2、4)()A15 B15C14 D14二、填空题8在二项式n的展开式中，各项系数之和为A，各项二项式系数之和为B，且AB72，则n_.9(2012大纲全国高考)若n的展开式中第3项与第7项的二项式系数相等，则该展开式中的系数为_10已知n的展开式中第5项的系数与第3项的系数比为563，则该展开式中x2的系数为_三、解答题11在n的展开式中，已知第6项为常数项(1)求n；(2)求含x2项的系数；(3)求展开式中所有的有理项12已知n，(1)若展开式中第5项，第6项与第7项的二项式系数成等差数列，求展开式中二项式系数最大项的系数；(2)若展开式前三项的二项式系数和等于79，求展开式中系数最大的项参考
3、答案一、选择题1B解析：二项式的通项为Tr1C()8r(2)r2rC，令0得r4，所以二项展开式的常数项为T524C，故选B2B解析：由题意可知，n10通项为Tr1C()10r2rCx，令0，得r2故其常数项为22C1803D解析：令x1得(1a)(21)52，a1的通项为Tr1C(2x)5r(1)r25rCx52r，令52r1，得r2令52r1，得r3，展开式的常数项为(1)223Ca(1)322C8040404D解析：由2n64，得n6于是，二项式的展开式的通项为Tr1Cx2(6r)(2)rCx123r，令123r0，得r4，故其常数项为(2)4C2405D解析：的通项为Tr1C(1)r(
4、1)rC要使(x22)的展开式为常数，须令102r2或0，此时r4或5故(x22)的展开式的常数项是(1)4C2(1)5C36C解析：由题意可知，2n128，解得n7的通项为Tr1C(3x)7r(1)r37rC，令73，得r6其系数为(1)6376C217D解析：令x0，得a01令x1，得a0a1a2a3a4a525；令x1，得a0a1a2a3a4a50两式相加得2(a0a2a4)25，a2a415，a0(a2a4)14二、填空题83解析：由题意可知，B2n，A4n，由AB72，得4n2n72，即2n8，n3956解析：CC，n8Tr1Cx8rCx82r，当82r2时，r5系数为C561018
5、0解析：由题意可知，解得n10在的展开式中，Tr1C()10r2rCx，令2，得r2所以x2的系数为22C180三、解答题11解：(1)通项为Tr1CxCx，第6项为常数项，r5时，有0，即n10.(2)令2，得r(n6)2，所求的系数为C(3)根据通项，由题意得令k(kZ)，则102r3k，即r5k，rZ，k应为偶数k可取2，0，2，此时r取2，5，8第3项，第6项与第9项为有理项，它们分别为Cx2，C，Cx212解：(1)通项Tr1C(2x)r22rnCxr，由题意知C，C，C成等差数列，2CCC，n14或7当n14时，第8项的二项式系数最大，该项的系数为22714C3 432；当n7时，
6、第4项和第5项的二项式系数相等且最大，其系数分别为2237C，2247C70(2)由题意知CCC79，n12或n13(舍)Tr122r12Cxr由22r12C22(r1)12C，22r12C22(r1)12C，得r10展开式中系数最大的项为T11221012Cx10(2x)10高考资源网版权所有！投稿可联系QQ：108459180129C91AFE4CED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFEDD1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91A
7、FE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF95AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9D1B6C8795AD9C91AFE4CED1B6C8795A1AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFC91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6CD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1
8、B6C8795AD29C91AF8795AD9C91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF5D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFAD9C91FE4CED1B6C8795AD29C91AFB6C8795AD29C91AFB6C8795AD29C91AFD1
9、B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFFE4CED1B6C8795AD29C91AFC8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD9C91AFED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8D1B6
10、C8795AD9C91AFE4CED1D91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFC91FE4CED1D1B6C871AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFC91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6CD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF8795AD9C91FE4CED1D1B
11、6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF5D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFAD9C91FE4CED1B6C8795AD29C91AFB6C8795AD29C91AFB6C8795AD29C91AFD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4
12、CED1B6D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8791AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFC91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6CD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF8795AD9C91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD
13、91AFE4CED1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF5D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFAD9C91FE4CED1B6C8795AD29C91AFB6C8795AD29C91AFB6C8795AD29C91AFD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6D1B6C8795AD9C91AFE4CED1
14、B6C8795AD91AFE4CED1B6C8795AD9C91D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFFE4CED1B6C8795AD29C91AFC8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD9C91AFED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8D1B6C8795AD9C91AFE4CED15AD9C91D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4C
15、ED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFFE4CED1B6C8795AD29C91AFC8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD9C91AFED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8D1B6C8795AD9C91AFE4CED195AD9C91AFE4CED1B6C8795AD91AFE4CED1B6CD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF8
16、795AD9C91FE4CED1D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF5D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFAD9C91FE4CED1B6C8795AD29C91AFB6C8795AD29C91AFB6C8795AD29C91AFD1B6C8795AD9C91AFE4
17、CED1B6C8795AD91AFE4CED1B6D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFFE4CED1B6C8795AD29C91AFC8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD9C91AFED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8D1B6C8795AD9C91AFE4CE
18、D1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF795AD9C91FE4CED1B6C8795ADD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF29C91AF4CED1B6C8795AD1B6C8795AD9C91AFE4CED1B6C8795AD91AFD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD9C91AFE4CED1B
19、6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD29C91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C9D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF1AFD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFD1BD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF4CED1B6C8795AD29C91AFE4CED1B6C8795ADC6F554C62
