首页
定义为n个正数p1,p2,…pn的“均倒数”.若已知数列{an}的前n项的“均倒数”为,又...
试题详情
定义
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAqCAYAAADLarc0AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
为n个正数p
1,p
2,…p
n的“均倒数”.若已知数列{a
n}的前n项的“均倒数”为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAjCAYAAABsFtHvAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEkSURBVFhH7VdRDsMgCOVk3snreBmO4lEY1OpU
tB+4zCyzSZNmLTweILwBbbxgIzb9KHgM5MBRiPbc2ZijJwDgewf4RRbJH3Bj2W01P2n/v4a7Boyc
83R7tHXcQsPZAGurA76eQ4MH7pd343zzWWI9NTdUbN0kpb2IA66/C7QgTsYRTVQPkLwoI0oEAgdg
GVlMYGj2oHogIjZMY3A29jPwh/Wru10i7TNR5nek4Cbz/BPg6PtFIaXwrNgEOAlGyY7jB/l2PhvE
Jl9jvdcyb+p/G8pv3ITBZ6Wa2Kv6rjEXp3W0CfzqgXpt3sGoE7ECjoVZfVo0y5xydaas4OKwSWN2
pFjmuiOF/q+KBXzcNCn9imVRMLo803n3oHrOYlnfEgYPW9P+AonhqEc68JjiAAAAAElFTkSuQmCC
)
,又
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAAqCAYAAAAAsVPKAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,则
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIYAAAAqCAYAAAB2pyMEAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
=( )
A.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACGSURBVEhLY/hPAWCgQO9/Gmm+P+u/HYPd/1n3
cbsNu837C/8zMDAAMTmawZbt/184qhkj2PHE84AEGDiBgOIZggv3Y08oNEqeROSYAbQZFiik0iBf
DaCziQhUnEoQzsZXcuCQg2jGV3LgkUMKMHwZAbvcqGacRS3NAgxfyYFHbshnDDKyFwB9poPffNQh
IwAAAABJRU5ErkJggg==
)
B.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADtSURBVEhL1VXRDcUgCGQyd3Idl3EUR+Ep6BNF
q76maV4TP9p4HBwHBbzxwA0sPgAODg0AAh2LfpLegNmjBYMuMCI4g2Ac5tcmjAZ7211OwQDtgF6B
NVNAZwBNSUVwa+Zcb2U6AZc6v4KxcFtp98KeCSbRqoQ29NwkSfWY7kioEmIqGIhezyz8gD03p+VF
Zp6c85MqezHtTWGH12raZMW6BOptnirSpVsKDM5WHLnK22pRGhIxXkKwdv0wc/+tfb8Gq5XEJRTy
S/BqJT0HJiEbhQ/Sjks7tk8u/RPBqIurVjW/l35Trkzyo0f/dKo+BBtPzjfUzRQAAAAASUVORK5C
YII=
)
C.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADISURBVEhL7VTJDcQgDHRl7ol23AylUMqEI2wg
cUAc+1hpI6GIOGOPryEsPLSAxSawEzAxxN25OAgTiPxhQWlOka1JRgVsDYFPj04YZOzHe0HbwjzA
92/1vQ0OjCqqKYUcvAmONBVwTuN74FjIWdqI7TO46jtSsNjFXqtihHMQ/LtopYf3hmRywDfN9kT0
tchpIcZPILoWeSJVbSXH3Vy0X5UkzImuMl0laalMR0lyKprKVNXWf0jwPziXcUO1W0rSsP38Yowv
FQ5dqkHBOutiKgAAAABJRU5ErkJggg==
)
D.
相关试题
-
定义:称
为n个正数a1,a2,…,an的“均倒数”,已知正项数列{an}的前n项的“均倒数”为
,则![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAhCAYAAAC4JqlRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVZJREFU
WEftl+uNxCAMhLmWaceduI5UQRNeBvP0KQl3yi77g0jRBgXwl7GB2R+Jl1t5AWDl5S6DBxbvnNCB
XkHYO/EcHuU9B8jBY3YWAaSP7hV49MPrZNcpkEOoKrAaoFcjPXvhoIBIk0uF0tqztTKnAGsqUj10
z85RDIm4pBBDO7+7EW4OQKO0dFQF8ux37QuIDfDNCujOp8V1dpuVYFdGKcr/18B71n4/600KNsBW
YCuwFfiIAsVEjGf7rKFQO4AteYQ9qDcq6NO2837uvBNGCM8SYCzgbMrvtAA4NzqIOF6dtJoVIhiW
ZlAC+/peAWInH50O5VGgBSU6Xh9Gvw8pHcfqlCqDtfOHcJYsAag8hdB8zZQK45gRACm2KRoATAfY
K6RjKnBR2QRIiuoMSUVi4XiXOccUmIB4+ZcCPONs6cvKdn90hiK0AUu1PgExI+L2A8sVeAGCIsE1
GYQnawAAAABJRU5ErkJggg==
)
( )
A.0
B.1
C.2
D.
-
定义:称
为n个正数a1,a2,…,an的“均倒数”,已知正项数列{an}的前n项的“均倒数”为
,则![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAhCAYAAAC4JqlRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVZJREFU
WEftl+uNxCAMhLmWaceduI5UQRNeBvP0KQl3yi77g0jRBgXwl7GB2R+Jl1t5AWDl5S6DBxbvnNCB
XkHYO/EcHuU9B8jBY3YWAaSP7hV49MPrZNcpkEOoKrAaoFcjPXvhoIBIk0uF0tqztTKnAGsqUj10
z85RDIm4pBBDO7+7EW4OQKO0dFQF8ux37QuIDfDNCujOp8V1dpuVYFdGKcr/18B71n4/600KNsBW
YCuwFfiIAsVEjGf7rKFQO4AteYQ9qDcq6NO2837uvBNGCM8SYCzgbMrvtAA4NzqIOF6dtJoVIhiW
ZlAC+/peAWInH50O5VGgBSU6Xh9Gvw8pHcfqlCqDtfOHcJYsAag8hdB8zZQK45gRACm2KRoATAfY
K6RjKnBR2QRIiuoMSUVi4XiXOccUmIB4+ZcCPONs6cvKdn90hiK0AUu1PgExI+L2A8sVeAGCIsE1
GYQnawAAAABJRU5ErkJggg==
)
( )
A.0
B.1
C.2
D.
-
定义:称
为n个正数a1,a2,…,an的“均倒数”,已知正项数列{an}的前n项的“均倒数”为
,则![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAhCAYAAAC4JqlRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAVZJREFU
WEftl+uNxCAMhLmWaceduI5UQRNeBvP0KQl3yi77g0jRBgXwl7GB2R+Jl1t5AWDl5S6DBxbvnNCB
XkHYO/EcHuU9B8jBY3YWAaSP7hV49MPrZNcpkEOoKrAaoFcjPXvhoIBIk0uF0tqztTKnAGsqUj10
z85RDIm4pBBDO7+7EW4OQKO0dFQF8ux37QuIDfDNCujOp8V1dpuVYFdGKcr/18B71n4/600KNsBW
YCuwFfiIAsVEjGf7rKFQO4AteYQ9qDcq6NO2837uvBNGCM8SYCzgbMrvtAA4NzqIOF6dtJoVIhiW
ZlAC+/peAWInH50O5VGgBSU6Xh9Gvw8pHcfqlCqDtfOHcJYsAag8hdB8zZQK45gRACm2KRoATAfY
K6RjKnBR2QRIiuoMSUVi4XiXOccUmIB4+ZcCPONs6cvKdn90hiK0AUu1PgExI+L2A8sVeAGCIsE1
GYQnawAAAABJRU5ErkJggg==
)
( )
A.0
B.1
C.2
D.
-
定义:称
为n个正数p1,p2,…pn的“均倒数”.若已知数列{an}的前n项的“均倒数”为
.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)设
,试求数列{dn}的前n项和Tn.
-
定义:称
为n个正数p1,p2,…pn的“均倒数”.若已知数列{an}的前n项的“均倒数”为
.
(1)求数列{an}的通项公式;
(2)设
,试判定数列{cn}的单调性;
(3)设
,试求数列{dn}的前n项和Tn.
-
定义
为n个正数p1,p2,…pn的“均倒数”.若已知数列{an}的前n项的“均倒数”为
,又
,则
=( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAI1JREFU
SEtj/A8EDOQCkGZyAQO5GsEuxqr51a7/RQxF/3e9wm80puYrs0FhAMTkaAZbduX/7FHNWIMdRzwP
SICBEwgoniF49hXcCYUGyZPIBD+ANsMChlQad5Yc/H6GuxBf6YFDDhJV+EoPPHJI8YwvM2CXG9WM
s7ilWYDhKz3wyA1gfiYy95FSbhNnJADLU1782CUllgAAAABJRU5ErkJggg==
)
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAPdJREFU
SEvVVdERwyAIpSu7jps4h1O4BFWIUdCY4rWXq3d+mPMJPB4vL8wLdlcB7y7YBVLGAzgFdACllLw9
xsXrChzRg8OQGJGCQ3ABj+PwjARHry6XxwD9RXgBHiMlDA7Q1VRUbBn5qLdFsoBrnSdhTNxHaWtG
bIT16KGEsWdzkRTWc7pXRNVnpoRB1+uVAr8sT4PYH4zM02Pf85H8j5rPLEmOzQha9jxZxIsyBm7V
IceZsqJvMqVB6Uas67O0II6sv8nzGjzYEpdQgy/Bd7b0OzARKRg2pJ2NO7evN34LYdTFu1aJX4x2
yzuRGIahv/qgGWxmTLA3kj8zcx5+eHAAAAAASUVORK5CYII=
)
C.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAANBJREFU
SEvtVdsNwyAMdFf2OmzCHEzBElcwIQVCQTG0X0GKosQ6+/w6XgiHtCeCtYe0QGF8gr0FE8P61p2H
ZYqpgdiiNCewM8nYATtD4MOjtwwy7vRe0HYwF3D7r/4egyOjimpKIQcfgoVmB5zT+B1YCqmlDWmf
wae+dwomXZy1SiIcgxDeRSsDfDYkyhndNNuK6GuR00Lcf+qV/DttRcDOPn9VkjgnfZWZKslIZSZK
khn2VKYUwLA7Vxl6wO2FsKHaIyUZ2NZWcs9sK7ws0X4DZ2oousItqVUAAAAASUVORK5CYII=
)
D.
-
定义
为n个正数p1,p2,…pn的“均倒数”.若已知数列{an}的前n项的“均倒数”为
,又
,则
=( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACGSURBVEhLY/hPAWCgQO9/Gmm+P+u/HYPd/1n3
cbsNu837C/8zMDAAMTmawZbt/184qhkj2PHE84AEGDiBgOIZggv3Y08oNEqeROSYAbQZFiik0iBf
DaCziQhUnEoQzsZXcuCQg2jGV3LgkUMKMHwZAbvcqGacRS3NAgxfyYFHbshnDDKyFwB9poPffNQh
IwAAAABJRU5ErkJggg==
)
B.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADtSURBVEhL1VXRDcUgCGQyd3Idl3EUR+Ep6BNF
q76maV4TP9p4HBwHBbzxwA0sPgAODg0AAh2LfpLegNmjBYMuMCI4g2Ac5tcmjAZ7211OwQDtgF6B
NVNAZwBNSUVwa+Zcb2U6AZc6v4KxcFtp98KeCSbRqoQ29NwkSfWY7kioEmIqGIhezyz8gD03p+VF
Zp6c85MqezHtTWGH12raZMW6BOptnirSpVsKDM5WHLnK22pRGhIxXkKwdv0wc/+tfb8Gq5XEJRTy
S/BqJT0HJiEbhQ/Sjks7tk8u/RPBqIurVjW/l35Trkzyo0f/dKo+BBtPzjfUzRQAAAAASUVORK5C
YII=
)
C.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAjCAYAAABLuFAHAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADISURBVEhL7VTJDcQgDHRl7ol23AylUMqEI2wg
cUAc+1hpI6GIOGOPryEsPLSAxSawEzAxxN25OAgTiPxhQWlOka1JRgVsDYFPj04YZOzHe0HbwjzA
92/1vQ0OjCqqKYUcvAmONBVwTuN74FjIWdqI7TO46jtSsNjFXqtihHMQ/LtopYf3hmRywDfN9kT0
tchpIcZPILoWeSJVbSXH3Vy0X5UkzImuMl0laalMR0lyKprKVNXWf0jwPziXcUO1W0rSsP38Yowv
FQ5dqkHBOutiKgAAAABJRU5ErkJggg==
)
D.
-
已知正数数列{an}(n∈N*)定义其“调和均数倒数”
(n∈N*),那么当
时,a2010=________.
-
已知正数数列{an}(n∈N*)定义其“调和均数倒数”
(n∈N*),那么当
时,a2010=________.
-
当p1,p2,…,pn均为正数时,称
为p1,p2,…,pn的“均倒数”、已知数列{an}的各项均为正数,且其前n项的“均倒数”为
,
(Ⅰ)试求数列{an}的通项公式;
(Ⅱ)设
,试判断并说明cn+1-cn(n∈N*)的符号;
(Ⅲ)已知
,记数列{bn}的前n项和为Sn,试求
的值.