首页
已知数列{an}的前n项和为Sn,满足,且.(1)令,确定bn与bn-1(n≥2)的关系;...
试题详情
已知数列{a
n}的前n项和为S
n,满足
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAgCAYAAADe16AYAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,且
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAjCAYAAADmOUiuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVhJREFU
WEftVtsRhCAM5FqmHTqhjlRBEzkCogQRYcAxHzI6N6cxLJvX/tAvJXkRQMlLSQYXoisGoLOolUbr
OCIZAMFQHfhbKsBAGqD5AE4l9MfgFH1fDs7SJ5zB0KSpD8bbwHFeGY26wf8ygOn0vb+9OcEAgkk0
GwQaPznXvR4X220AHVrtwe2AqGnyXFi8b7e7ADAwx9giwOfB3fLaG9pkl3y1votyK1SQD2m+Oz3T
Fgvl033qlYbKWY2aibAYbv5s5ZZjvhQPb8y9qMsc+ouvC1E5tuWY9RbirHqDLquIx4aoHNuyYr37
9vsWqTXYB+uSaAogRaXoHnnBvg7QAbBipJrIWXwd4In9YkCIA0hFOyEWHsjBsv8W41UQg9R/i4ER
JsnQeo5BMPXR2g+wISqHzlgxpsplkfWFkv73A5xFcfH9IfEORa0ybfA6wLtzfwDvGLp7L57BP6B9
KsI4Jk1sAAAAAElFTkSuQmCC
)
.
(1)令
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAjCAYAAADc6ffdAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,确定b
n与b
n-1(n≥2)的关系;
(2)求{a
n}的通项.
相关试题
-
已知数列{an}的前n项和为Sn,满足
,且
.
(1)令
,确定bn与bn-1(n≥2)的关系;
(2)求{an}的通项.
-
已知数列{an}与{bn}满足关系,a1=2a,an+1=
(an+
),
(n∈N+,a>0)
(l)求证:数列{log3bn}是等比数列;
(2)设Sn是数列{an}的前n项和,当n≥2时,
是否有确定的大小关系?若有,请加以证明,若没有,请说明理由.
-
已知:正数数列{an}的通项公式an=
(n∈N*)
(1)求数列{an}的最大项;
(2)设bn=
,确定实常数p,使得{bn}为等比数列;
(3)(理)数列{Cn},满足C1>-1,C1≠
,Cn+1=
,其中p为第(2)小题中确定的正常数,求证:对任意n∈N*,有C2n-1>
且C2n<
或C2n-1<
且C2n>
成立.
(文)设{bn}是满足第(2)小题的等比数列,求使不等式-b1+b2-b3+…+(-1)nbn≥2010成立的最小正整数n.
-
已知数列{an}、{bn}的前n项和分别为Sn、Tn,且满足2Sn=-2an+n2-n+2,2bn=n-2-an.
(Ⅰ)求a1、b1的值,并证明数列{bn}是等比数列;
(Ⅱ)试确定实数λ的值,使数列
是等差数列.
-
已知数列{an}的前n项和为{Sn},又有数列{bn}满足关系b1=a1,对n∈N*,有an+Sn=n,bn+1=an+1-an
(1)求证:{bn}是等比数列,并写出它的通项公式;
(2)是否存在常数c,使得数列{Sn+cn+1}为等比数列?若存在,求出c的值;若不存在,说明理由.
-
已知Sn是数列{an}的前n项和,Sn满足关系式
,
(n≥2,n为正整数).
(1)令bn=2nan,求证数列{bn}是等差数列,
(2)求数列{an}的通项公式;
(3)对于数列{un},若存在常数M>0,对任意的n∈N*,恒有|un+1-un|+|un-un-1|+…|u2-u1|≤M成立,称数列{un}为“差绝对和有界数列”,证明:数列{an}为“差绝对和有界数列”;
-
已知Sn是数列{an }的前n项和,Sn满足关系式
,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAjCAYAAADmOUiuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVhJREFU
WEftVtsRhCAM5FqmHTqhjlRBEzkCogQRYcAxHzI6N6cxLJvX/tAvJXkRQMlLSQYXoisGoLOolUbr
OCIZAMFQHfhbKsBAGqD5AE4l9MfgFH1fDs7SJ5zB0KSpD8bbwHFeGY26wf8ygOn0vb+9OcEAgkk0
GwQaPznXvR4X220AHVrtwe2AqGnyXFi8b7e7ADAwx9giwOfB3fLaG9pkl3y1votyK1SQD2m+Oz3T
Fgvl033qlYbKWY2aibAYbv5s5ZZjvhQPb8y9qMsc+ouvC1E5tuWY9RbirHqDLquIx4aoHNuyYr37
9vsWqTXYB+uSaAogRaXoHnnBvg7QAbBipJrIWXwd4In9YkCIA0hFOyEWHsjBsv8W41UQg9R/i4ER
JsnQeo5BMPXR2g+wISqHzlgxpsplkfWFkv73A5xFcfH9IfEORa0ybfA6wLtzfwDvGLp7L57BP6B9
KsI4Jk1sAAAAAElFTkSuQmCC
)
(n≥2,n为正整数).
(1)令bn=2nan,求证数列{bn }是等差数列,并求数列{an}的通项公式;
(2)对于数列{un},若存在常数M>0,对任意的n∈N*,恒有|un+1-un|+|un-un-1|+…+|u2-u1|≤M成立,称数列{un} 为“差绝对和有界数列”,
证明:数列{an}为“差绝对和有界数列”;
(3)根据(2)“差绝对和有界数列”的定义,当数列{cn}为“差绝对和有界数列”时,
证明:数列{cn•an}也是“差绝对和有界数列”.
-
已知Sn是数列{an}的前n项和,Sn满足关系式
,
(n≥2,n为正整数).
(1)令bn=2nan,求证数列{bn}是等差数列,
(2)求数列{an}的通项公式;
(3)对于数列{un},若存在常数M>0,对任意的n∈N*,恒有|un+1-un|+|un-un-1|+…|u2-u1|≤M成立,称数列{un}为“差绝对和有界数列”,证明:数列{an}为“差绝对和有界数列”;
-
已知Sn是数列{an }的前n项和,Sn满足关系式
,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAjCAYAAADmOUiuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVhJREFU
WEftVtsRhCAM5FqmHTqhjlRBEzkCogQRYcAxHzI6N6cxLJvX/tAvJXkRQMlLSQYXoisGoLOolUbr
OCIZAMFQHfhbKsBAGqD5AE4l9MfgFH1fDs7SJ5zB0KSpD8bbwHFeGY26wf8ygOn0vb+9OcEAgkk0
GwQaPznXvR4X220AHVrtwe2AqGnyXFi8b7e7ADAwx9giwOfB3fLaG9pkl3y1votyK1SQD2m+Oz3T
Fgvl033qlYbKWY2aibAYbv5s5ZZjvhQPb8y9qMsc+ouvC1E5tuWY9RbirHqDLquIx4aoHNuyYr37
9vsWqTXYB+uSaAogRaXoHnnBvg7QAbBipJrIWXwd4In9YkCIA0hFOyEWHsjBsv8W41UQg9R/i4ER
JsnQeo5BMPXR2g+wISqHzlgxpsplkfWFkv73A5xFcfH9IfEORa0ybfA6wLtzfwDvGLp7L57BP6B9
KsI4Jk1sAAAAAElFTkSuQmCC
)
(n≥2,n为正整数).
(1)令bn=2nan,求证数列{bn }是等差数列,并求数列{an}的通项公式;
(2)对于数列{un},若存在常数M>0,对任意的n∈N*,恒有|un+1-un|+|un-un-1|+…+|u2-u1|≤M成立,称数列{un} 为“差绝对和有界数列”,
证明:数列{an}为“差绝对和有界数列”;
(3)根据(2)“差绝对和有界数列”的定义,当数列{cn}为“差绝对和有界数列”时,
证明:数列{cn•an}也是“差绝对和有界数列”.
-
已知Sn是数列{an }的前n项和,Sn满足关系式
,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAjCAYAAADmOUiuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVhJREFU
WEftVtsRhCAM5FqmHTqhjlRBEzkCogQRYcAxHzI6N6cxLJvX/tAvJXkRQMlLSQYXoisGoLOolUbr
OCIZAMFQHfhbKsBAGqD5AE4l9MfgFH1fDs7SJ5zB0KSpD8bbwHFeGY26wf8ygOn0vb+9OcEAgkk0
GwQaPznXvR4X220AHVrtwe2AqGnyXFi8b7e7ADAwx9giwOfB3fLaG9pkl3y1votyK1SQD2m+Oz3T
Fgvl033qlYbKWY2aibAYbv5s5ZZjvhQPb8y9qMsc+ouvC1E5tuWY9RbirHqDLquIx4aoHNuyYr37
9vsWqTXYB+uSaAogRaXoHnnBvg7QAbBipJrIWXwd4In9YkCIA0hFOyEWHsjBsv8W41UQg9R/i4ER
JsnQeo5BMPXR2g+wISqHzlgxpsplkfWFkv73A5xFcfH9IfEORa0ybfA6wLtzfwDvGLp7L57BP6B9
KsI4Jk1sAAAAAElFTkSuQmCC
)
(n≥2,n为正整数).
(1)令bn=2nan,求证数列{bn }是等差数列,并求数列{an}的通项公式;
(2)对于数列{un},若存在常数M>0,对任意的n∈N*,恒有|un+1-un|+|un-un-1|+…+|u2-u1|≤M成立,称数列{un} 为“差绝对和有界数列”,
证明:数列{an}为“差绝对和有界数列”;
(3)根据(2)“差绝对和有界数列”的定义,当数列{cn}为“差绝对和有界数列”时,
证明:数列{cn•an}也是“差绝对和有界数列”.