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1、高一數(shù)學(xué)期末復(fù)習(xí)綜合測試 數(shù)列通項(xiàng)與求和一、選擇題1(1997上海高考)設(shè)f(n)= 1,那么f(n+1)f(n)等于 ( ) A. B. C. D. +2. 設(shè)等差數(shù)列an的公差為d,如果它的前n項(xiàng)和sn = n2 ,那么 ( ) A. an = 2n1 , d = 2 B. an = 2n1 , d = 2 C. an = 2n1 , d = 2 D. an = 2n1 , d = 23. (2000北京春招)已知等差數(shù)列an滿足a1a2a101 = 0 ,則有 ( ) A. a1a1010 B. a2a1000 C. a3a99 = 0 D. a51 = 514. 數(shù)列an中, ,若sn
2、 = 9 ,則n等于 ( ) A. 9 B. 10 C. 99 D. 1005. 數(shù)列an滿足anan-1 = an-1+(1)n (n2)且a1 = 1 ,則a5a3等于 ( ) A B. C. D . 6Sn=12+23+34+n(n+1)等于 ( )A(n+1)(n+1)2-1 B(n+1)(n+1)2-1C(n+1)(n+2)(2n+1) Dn(n-1)(2n+1)二、填空題7. 已知數(shù)列an的前n項(xiàng)和sn滿足log2(sn+1)= n+1 ,則an = 。8數(shù)列an滿足a1+2a2+(n1)an-1+nan = n(n+1)(n+2),則an = _.9. ( 2000全國高考)設(shè)數(shù)
3、列an是首項(xiàng)為1的正項(xiàng)數(shù)列,且(n+1)an+12nan2+an+1an = 0(n = 0,1,2,3,),則它的通項(xiàng)公式為an = 。10、已知數(shù)列an的通項(xiàng)公式為an=2n-2n+1,則該數(shù)列前n項(xiàng)和sn_。三、解答題11數(shù)列an中,a1 = ,當(dāng)n2時(shí),有(3n22n1)an = a1+a2+an-1(1) 求an ;(2) 求數(shù)列an的前n項(xiàng)和為sn。12設(shè)數(shù)列an的前n項(xiàng)和為sn ,且a1 =1,sn+1= 4an+2 (1) 設(shè)bn = an+12an , 求證bn是等比數(shù)列; (2) 設(shè)cn = ,求證cn是等差數(shù)列; (3) 求sn = a1+a2+an-1+an。13.已知數(shù)列an的通項(xiàng)公式滿足:n為奇數(shù)時(shí),an=6n-5 ,n為偶數(shù)時(shí),an=4 n ,求sn.