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已知数列{an}的前n项和为Sn,若.(1)求证:{an-1}为等比数列;(2)求数列{b...
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已知数列{a
n}的前n项和为S
n,若
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALQAAAAxCAYAAABzsINZAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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vpuajdgcDl6V1yof2mVG4tR3GVxvR6VekiqL+drpgIQ2FnG3VHsKs1Qoi4bmG2SkaYbv1S8WQEJL
SAVIskjbJDOoSQ386iB6vEFGhDqPmvaJBZzQqkh73rTPrcsA27LQSqj2ZXxEUkTn4lhQXkmi9EHo
LO8k0OZuNCTnuwtQCdLt3iBjWos8LYpiQXklidKHAAWQ0JfA/ZOkBkFIWJc3yAjT5HmrkljgX0kS
ha7ol5WoGMAIfSFwydoGqiKiOFilrE1YukkZycohO5bEgvJKEqUPUmXTHEToKzmyvbtAFDrU7Q0y
ZlQ3OlRJLCivJFH6ULECEZo6OPf7HgKUV5IofSDIhQITTGgIctzmRIDyShKlzzGj8L/FEwjXz92T
Y0xoJmvjCIQJLYUOFo41rg2L9yoEKK8kpfowoV9FgU8JS3klKdjnT2Sl04+hs4X+FHvaVIbySlK8
D1voNle6C6korySl+jChu6BOk0pSXklK9mFCN7nWPQjlJFCAryRR+pgIh6ktt4vkOGzXA9M60pEJ
3dFi96AqE7qHVe5Ix//zcsm04CHiVgAAAABJRU5ErkJggg==
)
.
(1)求证:{a
n-1}为等比数列;
(2)求数列{b
n}的前n项和.
相关试题
-
已知f(x)=x2+2x,数列{an}满足a1=3,an+1=f′(an)-n-1,数列{bn}满足b1=2,bn+1=f(bn).
(1)求证:数列{an-n}为等比数列;
(2)令
,求证:
;
(3)求证:
-
已知数列{an}是等差数列,a3=10,a6=22,数列{bn}的前n项和是Tn,且
.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:数列{bn}是等比数列;
(Ⅲ)记cn=an•bn,求证:cn+1<cn.
-
已知数列{an}是等差数列,a3=10,a6=22,数列{bn}的前n项和是Tn,且
.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:数列{bn}是等比数列;
(Ⅲ)记cn=an•bn,求证:cn+1<cn.
-
已知数列{an}是等差数列,a3=10,a6=22,数列{bn}的前n项和是Tn,且
.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:数列{bn}是等比数列;
(Ⅲ)记cn=an•bn,求证:cn+1<cn.
-
已知数列{bn}中,
,bn+1bn=bn+2.数列{an}满足:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHQAAAAqCAYAAABiHn+gAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAA7xJREFU
eF7tW9mVhCAQdFMmHTIhDqIwCbebQ7kUZFoRxffmY98wHFXd1Qfu3wLPNJ73IICEjuc9CEzvOco4
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86+LYJjhEGzyzyA0j1HDEUjktHA5L4KLZVZJ4TGxg9CGdJUuLTlm9vDheR8dhJai2mTc2z1UNRWM
tSopaoJyg0VfHUMb4NnRkh1KLjG6mGh06uqSxx2zbxOKZDLIHglsRLck059oeid0sKApvSZARUkQ
ZL/MDz3fJRRBJSDTklhjE5q8uAyZBTuRH/itUDJCjyw09Z0F4Ozvfh1v10UwKZQW91P3ABGcmzrT
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sqrPz1iN3G4eiiI7+XLrAjuDxdxFqIklBGWENlhQHRtCTM3nx8Cdtx4ib7ShR4JEHoNRXoemZVXx
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2b2fHaDaWJDhaUsnAtBuIiWxqdzh7KYfMd5PYB9CqFEFY2VURb/Fe9f7CVt/bbitbv1ZGTaeY6Qj
VZtVHSxoYuRaX16/M+yfRu0f2PtRbHLjbdXm2/0oZfgnPNQAY8En7CT5twbna+AjSCW01z5zbQpA
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89BW54TeI75czKCTLaDPKV/TDLgO0GcTqnIZp2lNWCpdB2nbmR9OqE7G8F8B8KHuILWF/prVn02o
65FDboss4NGEeh5pbyq+UEwWUZce9GhCfzjXZ386CH0Z9YPQlxH6DyBJOW/xmG2uAAAAAElFTkSu
QmCC
)
(Ⅰ)求证:an+1+2an+1=0;
(Ⅱ) 求数列{an}的通项公式;
(Ⅲ) 求证:(-1)b1+(-1)2b2+…+(-1)nbn<1(n∈N*)
-
已知数列{an}中,
,设
.
(Ⅰ)试写出数列{bn}的前三项;
(Ⅱ)求证:数列{bn}是等比数列,并求数列{an}的通项公式an;
(Ⅲ)设{an}的前n项和为Sn,求证:
.
-
已知两数列{an},{bn}(其中bn>0,且bn≠1),满足
且![](https://img.xintiku.com/upload/28/7f/287f37e882522e9f1f57911241773378.png)
(I)求证:an>bn
(II)求证:数列{an}的单调递减且
.
-
已知数列{an}中,a1=3,an+1=2an-1(n≥1).
(Ⅰ)设bn=an-1(n=1,2,3,…),求证:数列{bn}是等比数列;
(Ⅱ)设cn=
,求证:数列{cn}的前n项和Sn<
.
-
已知数列{an},{bn},满足条件an+1=2an+k(k≠0),bn=an+1-an≠0.
(1)求证:数列{bn}是等比数列;
(2)若k=a1=1,求数列{an},{bn}的通项公式.
-
已知数列{an}的前n项和为Sn,满足Sn=2an-2n(n∈N+),
(1)求证数列{an+2}为等比数列;
(2)若数列{bn}满足bn=log2(an+2),Tn为数列
的前n项和,求证:
.