2010-2011學(xué)年浙江省杭州市源清中學(xué)高一(下)數(shù)學(xué)暑假作業(yè)試卷
發(fā)布:2024/4/20 14:35:0
一、數(shù)列部分
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1.在數(shù)1和100之間插入n個(gè)實(shí)數(shù),使得這n+2個(gè)數(shù)構(gòu)成遞增的等比數(shù)列,將這n+2個(gè)數(shù)的乘積計(jì)作Tn,再令an=lgTn,n≥1.
(Ⅰ)求數(shù)列{an}的通項(xiàng)公式;
(Ⅱ)設(shè)bn=tanan?tanan+1,求數(shù)列{bn}的前n項(xiàng)和Sn.組卷:896引用:11難度:0.5 -
2.若數(shù)列An:a1,a2,…,an(n≥2)滿足|ak+1-ak|=1(k=1,2,…,n-1),則稱An為E數(shù)列,記S(An)=a1+a2+…+an.
(Ⅰ)寫出一個(gè)E數(shù)列A5滿足a1=a3=0;
(Ⅱ)若a1=12,n=2000,證明:E數(shù)列An是遞增數(shù)列的充要條件是an=2011;
(Ⅲ)在a1=4的E數(shù)列An中,求使得S(An)=0成立得n的最小值.組卷:436引用:2難度:0.1 -
3.已知等差數(shù)列{an}中,a1=1,a3=-3.
(Ⅰ)求數(shù)列{an}的通項(xiàng)公式;
(Ⅱ)若數(shù)列{an}的前k項(xiàng)和Sk=-35,求k的值.組卷:1760引用:66難度:0.5 -
4.設(shè)b>0,數(shù)列{an}滿足a1=b,an=
(n≥2)nban-1an-1+n-1
(1)求數(shù)列{an}的通項(xiàng)公式;
(2)證明:對(duì)于一切正整數(shù)n,2an≤bn+1+1.組卷:959引用:3難度:0.5
一、數(shù)列部分
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12.等比數(shù)列{an}的各項(xiàng)均為正數(shù),且2a1+3a2=1,a32=9a2a6,
(Ⅰ)求數(shù)列{an}的通項(xiàng)公式;
(Ⅱ)設(shè)bn=log3a1+log3a2+…+log3an,求數(shù)列{}的前n項(xiàng)和.1bn組卷:7087引用:137難度:0.5 -
13.已知公差不為0的等差數(shù)列{an}的首項(xiàng)a1(a1∈R),且
,1a1,1a2成等比數(shù)列.1a4
(Ⅰ)求數(shù)列{an}的通項(xiàng)公式;
(Ⅱ)對(duì)n∈N*,試比較與1a2+1a22+1a23+…+1a2n的大?。?/h2>1a1組卷:633引用:12難度:0.3