第4章4.4第1課時(shí)二項(xiàng)式定理123456789101112131415161718A級(jí)必備知識(shí)基礎(chǔ)練1.(1-2x)6展開式中,x3的系數(shù)為(

)A.20 B.-20 C.160

D.-160D1234567891011121314151617182.在(x-)6的二項(xiàng)展開式中,常數(shù)項(xiàng)為(

)A.256 B.240

C.192

D.160B1234567891011121314151617183.S=(x-1)4+4(x-1)3+6(x-1)2+4x-3,則S=(

)A.x4

B.x4+1 C.(x-2)4

D.x4+4A1234567891011121314151617184.若(1+3x)n(n∈N+)的二項(xiàng)展開式中,第三項(xiàng)的二項(xiàng)式系數(shù)為6,則第四項(xiàng)的系數(shù)為(

)A.4 B.27

C.36

D.108D1234567891011121314151617185.(1-)(1+x)6展開式中x2的系數(shù)為(

)A.-5 B.5

C.15

D.30A1234567891011121314151617186.在(x2-)9的二項(xiàng)展開式中,第4項(xiàng)的二項(xiàng)式系數(shù)是

,第4項(xiàng)的系數(shù)是

.

84123456789101112131415161718-21234567891011121314151617188.已知()n的二項(xiàng)展開式中,第2項(xiàng)與第4項(xiàng)的二項(xiàng)式系數(shù)之比為1∶12.(1)求正整數(shù)n的值;(2)求二項(xiàng)展開式中的常數(shù)項(xiàng).解

(1)∵第2項(xiàng)與第4項(xiàng)的二項(xiàng)式系數(shù)之比為1∶12,123456789101112131415161718B級(jí)關(guān)鍵能力提升練9.使(3x+)n(n∈N+)的展開式中含有常數(shù)項(xiàng)的最小的n為(

)A.4 B.5

C.6 D.7B12345678910111213141516171810.已知(1+ax)(1+x)5的展開式中x3的系數(shù)為15,則a的值為(

)C12345678910111213141516171811.(多選題)若(x+)6展開式中的常數(shù)項(xiàng)為15,則實(shí)數(shù)m的值可能為(

)A.1 B.-1 C.2 D.-2AB123456789101112131415161718ACD12345678910111213141516171813.(多選題)若(x-)n的展開式中含x2的項(xiàng),則n的取值可能為(

)A.6 B.8

C.10

D.14BD12345678910111213141516171814.對(duì)于(+x3)n(n∈N+),有以下四種判斷:①存在n∈N+,展開式中有常數(shù)項(xiàng);②對(duì)任意n∈N+,展開式中沒有常數(shù)項(xiàng);③對(duì)任意n∈N+,展開式中沒有x的一次項(xiàng);④存在n∈N+,展開式中有x的一次項(xiàng).其中正確的是(

)A.①③

B.②③ C.②④

D.①④D1234567891011121314151617185612345678910111213141516171860123456789101112131415161718(1)n的值;(2)展開式中含x3的項(xiàng);(3)二項(xiàng)展開式的常數(shù)項(xiàng);(4)二項(xiàng)展開式的所有有理項(xiàng).123456789101112131415161718(4)求展開式的有理項(xiàng),則

為整數(shù),即r為奇數(shù).因?yàn)?≤r≤9,可得r=1,3,5,7,9,則二項(xiàng)展開式中的所有有理項(xiàng)為T2=-18x3,T4=-672,T6=-4

032x-3,T8=-4

608x-6,T10=-512x-9.1234567891011121314151