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已知等差数列{an}的前n项和为Sn,且(2n-1)Sn+1-(2n+1)Sn=4n2-1...
试题详情
已知等差数列{a
n}的前n项和为S
n,且(2n-1)S
n+1-(2n+1)S
n=4n
2-1(n∈N
*).
(Ⅰ)求数列{a
n}的通项公式;
(Ⅱ)求证:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMYAAAAsCAYAAAA+RMe5AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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4uCSJpVAxnG+WTdGGNlE/Qfm20vR1jtybgAAAABJRU5ErkJggg==
)
.
相关试题
-
已知数列{an}的前项的和Sn满足Sn=2n-1(n∈N*),则数列{an2}的前项的和为( )
A.4n-1
B.
(4n-1)
C.
(4n-1)
D.(2n-1)2
-
已知等差数列{an}的前n项和为Sn,且(2n-1)Sn+1-(2n+1)Sn=4n2-1(n∈N*).
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:
.
-
已知等差数列{an}的前n项和为Sn,且(2n-1)Sn+1-(2n+1)Sn=4n2-1(n∈N*).
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:
.
-
已知等差数列{an}的前n项和为Sn,且(2n-1)Sn+1-(2n+1)Sn=4n2-1(n∈N*).
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:
.
-
已知数列{an}满足a1=-1,an+1-2an-3=0数列{bn}满足bn=log2(an+3).
(1)求{bn}的通项公式;
(2)若数列{2n+1bn}的前n项的和为sn,试比较sn与8n2-4n的大小.
-
(理)已知等比数列{an}的前n项和Sn=2n-1,则a12+a22+…+an2等于( )
A.(2n-1)2
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAjCAYAAADbqynIAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAHlSURBVFhH7VgJsoMgDOVk3InrcBmPwlFoIogs
kYQqU+vYmU7nt4h5yVvwK/+wl3oYHv9gQM56rbS37r9nFia0GK+UgvdTAAVU3ryA7kfPzBTeCTHj
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xbT7BUBrqOLNwzs2tCQGgkH65N+m/ILr6t/qGMB7NGuE3DsMfWxSWa/s6EMVg98l5NEA8k5U1zir
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qIaaYh//rtlNu+mzETEX+ruWYI/jjYNflFQiiyz0NNZ72WoZIIwEdkI8IOyOgJKyyg9WXQhoTfeO
3VJZcKp28mIZIGQqO6HeYwVOr6A7gCcz7DRCDtBuXG2wEhVRgt9suNTgBOpJQz/WDYDiATKcttYT
coMps8XTzb58g/JIpbxzRUAe2q/Qvi+vt7shd/ThwnG6PY+1g2p+MoWkiTmqHqv0xOrS5aIAZz+z
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fQBTCewATdcN+QAAAABJRU5ErkJggg==
)
C.4n-1
D.
-
(理)已知等比数列{an}的前n项和Sn=2n-1,则a12+a22+…+an2等于( )
A.(2n-1)2
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAjCAYAAADbqynIAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAGwSURBVFhH7ZYLsoMgDEVZGXtiO2yGpbCUNOEn
nyjokzfoeGeYVlvTnCQXKuBl+oBW1wZkNUghQdtw/VB5IKNACIHrLUBOBtQHtJ4+oHFRPPKlwnd0
6X0qJ1dscocwptRgCUYhVnydqLlACCC1BhUgjFqtQycrTABp5MCClvcWzKg2ngdyhyr9uF9szgRD
4xMunehefK7+rC4Q/UbznUHtHvpUpDLfrEMH4pKheykSJY9QeeTqGavltXFLRdvrblm4ISAanbpr
1pgCkBLOu1QD+PG76qGOHTIrDABRsOiDA5301zl1gNxI+hz7QJx3GHFdPFLsGLuaQB0gzC56CZ9n
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)
C.4n-1
D.
-
(理)已知等比数列{an}的前n项和Sn=2n-1,则a12+a22+…+an2等于( )
A.(2n-1)2
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAjCAYAAADbqynIAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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==
)
C.4n-1
D.
-
(理)已知等比数列{an}的前n项和Sn=2n-1,则a12+a22+…+an2等于( )
A.(2n-1)2
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAjCAYAAADbqynIAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAHlSURBVFhH7VgJsoMgDOVk3InrcBmPwlFoIogs
kYQqU+vYmU7nt4h5yVvwK/+wl3oYHv9gQM56rbS37r9nFia0GK+UgvdTAAVU3ryA7kfPzBTeCTHj
wQahLg2Qedepnuw6kycEoLT1Dk3HAKztcyJT5wICANpabxDMOiQFf8/NhTFAgx1GAIly3nmrr42F
xbT7BUBrqOLNwzs2tCQGgkH65N+m/ILr6t/qGMB7NGuE3DsMfWxSWa/s6EMVg98l5NEA8k5U1zir
v6MbG/qlO4sAIXXqqbllKaaFBedTqgEE+n2rISZSMikIAOFm0Xp7DBnUl5BscRkDaKVkqJEHRGmH
qIaaYh//rtlNu+mzETEX+ruWYI/jjYNflFQiiyz0NNZ72WoZIIwEdkI8IOyOgJKyyg9WXQhoTfeO
3VJZcKp28mIZIGQqO6HeYwVOr6A7gCcz7DRCDtBuXG2wEhVRgt9suNTgBOpJQz/WDYDiATKcttYT
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nKiXvbSxbT5I2T1/uqDNIU5HPy2Xv3kFqHUNfot7rVD7f007T6v3qrlbjeDo80dooNQX0N3n9bgJ
fQBTCewATdcN+QAAAABJRU5ErkJggg==
)
C.4n-1
D.
-
(理)已知等比数列{an}的前n项和Sn=2n-1,则a12+a22+…+an2等于( )
A.(2n-1)2
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAjCAYAAADbqynIAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAHlSURBVFhH7VgJsoMgDOVk3InrcBmPwlFoIogs
kYQqU+vYmU7nt4h5yVvwK/+wl3oYHv9gQM56rbS37r9nFia0GK+UgvdTAAVU3ryA7kfPzBTeCTHj
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coMps8XTzb58g/JIpbxzRUAe2q/Qvi+vt7shd/ThwnG6PY+1g2p+MoWkiTmqHqv0xOrS5aIAZz+z
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fQBTCewATdcN+QAAAABJRU5ErkJggg==
)
C.4n-1
D.