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已知函数F(x)=,(x),(I)求F()+F()+…+F()的值;(II)已知数列{an...
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已知函数F(x)=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAjCAYAAACD1LrRAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAF5SURBVFhH5VZRssMgCPRk3smTvH8v41E8Ck9i
JGgwoSUdP9KZTDspsrKLuA4WfdwiXFgMnCN458DhE9JzJKRQc+LjI2SWuVScINDL8rsEPYKNxVCi
mpcX5SDnbicpPAOcU+ry5ui7qnuNkRpebqNqYGSkTaXNkJuAsVJZ4wzRe4gZ6QpFmPqh+KYh/xa0
GpnsK96bzEfeBgAbTQxUVSEP6vSuf5yO06jFFoULh67UgyNjB1Nt3fkcjzojraVi75BuPVyLTEFe
NwDj7vquRgZQMtKobEx73Npa2i5b60rG45CzM9yah/RucUpUufkOyhePzM+lM694YcV0e0gT6Efv
xAFiFk+Z4IUa71fN1CkomZuHbRfPeWwWI3DtFEzANBUF4DunYAKudJZ7XKp4zMxvp0cciBL47Lms
DkQDLDiF6gMsDuQWWHYKdgdyAzxzClt7GBzIZXNdOQWLA6l9O6l45hT+drv7rQMhidhFw83LW2e1
fTx9nGEZ1f8Xi7hmgEATkQAAAABJRU5ErkJggg==
)
,(x
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAADySURBVEhL7ZXhDYNACIVvstuJdViGUW4UCtqe
cOiJbdOkTU2MP9TPx+OBhV88yovv8wcBDbmWyti85pwCAi6lyPksYPkoMfwBX+WB9B3IBGYJkeZg
Pe293SARgHQ9d+wAiHHM64QVAYQh7zMtBetW26PGfq3Iw+wEllcgZsEgP0CNmUpzgIZwSf4CeF8J
Ih+zvTNO9BKmve8LRQwfjL0DZFm46A0p7Pd0qQjEPLsCJr1vRK6VDatTkduJtvtaTlCQi/0qFhLD
dMjTqRy8ulBCY6xxStMAgvhPCFE+kq7OO+Vm4ZwqUNPiQG2lnALOGvQDgBvrsQn3mFOLQQAAAABJ
RU5ErkJggg==
)
),
(I)求F(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAjCAYAAABo4wHSAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEmSURBVFhH7VaLDYQgDO1k7MQ6LNNRGKXXgpz0
QAQvaEwwMTFCeX2vHwr0wAMPYNKLQL0jA4acv6bTOFO0BAD83gkayCHZBdoR5vGYLnk7ZE1bXiJv
aAxSp/G1OEBx23qR6ThQbrFA/9PvxJpzYU+KO77FnxXTuTGN/TtdzBxf40gPBJ6c2eJerLHt4RRx
bAfB6NtW5HJmgKzNoAUy21zinVFru7PlFNGyA4+omIWDv4x+J4TaxNDzT+8ps1ekTkzlW0kaJdP9
tgJ6YleAiizpUM1agh9Bk9wx20rQMzsNquIrOZJLPQVUWFj2O3tmy4u2MseGcsgd6UmaVEbHdkFe
kVElBzPcc6lRMo0hrVkyslg2+tzLRnNoThGt5jC14dUPX7fMVNE/RxltBU/HemoAAAAASUVORK5C
YII=
)
)+F(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAjCAYAAABo4wHSAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFASURBVFhH7VYBDoMgDOzL+BPf4TM8had0FtSB
YKFFYxa3xGQa6tnrcRzgAz94ABN/BNRbBIB0GYdBQZWs0+DQWL/CeLQEvN+Po4tAg/dFZ8EZVbci
0KoXovruTo+g3gIqMCfUW8x3fJ60UklvQGcsbpKSQSpBvTXoNHtl/Tpxp6TYYo6LmKRzFYGScHZj
2AwC5DSLQKWzO1v/B72KyeZ7Fl20xHHfswlzmCPibUJi0wD5LJMUyPihZYvndYCdNEAuZFajjYd2
7nn7x9agXB3waYAiSf7C4z0JauRZuaYWUp4G6H8RvhJlpcE3QDt1FWieBuoMlEA3utPGqUF7dSXo
IQ30ii8AbaSBu+ltpoG4HfLzckQ0S/+dukgvlwbYLXMy0zhpZqtBPw0w5hA7+h4Opao5c5jzblX1
2wxfRZK+6ANQhmN8mRCCgQAAAABJRU5ErkJggg==
)
)+…+F(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAjCAYAAABo4wHSAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFySURBVFhH7VfdmQMhCKQye7Idm7EUS+EWEZXV
Y38vPuTyfXmILIyMIzsBXPCBBZi4EDR6BAD+uoBJtZ8wuBuxFNBJTfAYu5qAFPSyFNHTg/U3YvSA
LvA2UnAnY1THYUnjvK4ZSDGqzvQDOnnbQlfMiBFzijFuRnoZz5QSJDokM9U5bMT2nW0c5TxhbAAl
OgXTSjYLl/Nsp2SBqvMtZ6hoaslH3eR4FRILcUIvFdQqsyg0Y7vLPwhJ4tE3tdWcTFO/kU48VqwH
HahGHg60k+6WZJE0Ld25MgW13H8RkOwFSDh77kF1d2M41MEwYW9DXjgGPzz1v6jTUUQzYb23Rif5
RfR+WLgZjum97RzyONtG5WwI/D5UHjmHttkR1HIcD5xDfVUoa8KrluOYqfesc6hi2APYrmJ6Zc46
hybAEfToBa/v6QXn8BLoRefwBr2XnYMFeuAqHjmHuVLLqmHSnzkH9dehuT2GtYbDgjn4/5b5U9J/
AOE7mOhrhEyiAAAAAElFTkSuQmCC
)
)的值;
(II)已知数列{an}满足a
1=2,a
n+1=F(a
n),求证数列{
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqCAYAAABP7FAaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAE9SURBVFhH7ZaLDYQgDIaZrDuxDsswCqP0WtAc
qLyKeDGHiYmJ6Ef/PvgV/uBSP2Dii6DOIChA42Q69UdqNSql6H4S6oOzqBe0Ic39OV3yNsi6L3mJ
vH4wcJ+GW9uOELelwkj7QfEXCzqmX+VrqoVvUTzxzPtZOZ2b06l/z/x8bk4ztmYetGBr5kEL524E
Zd+zGS7LQ12TExq9rr1UgCbaOzRAcMnxcdpjFhogMcNqhVAwtfw+O72SzeagnPBkIW9C7mnTYDNQ
3nXMdAZQgUGheT8I3AD1QCqmkrR9pVWSdztpGLbnaxhcsDWT+/Ralwp0612f4/i5T+Tj6jLUOXRU
3WAsVTQNCy/Z+NCoyut7loC+bU/tJYu4QV6glgoNdGwvGbJmV+LIbpK26pGSyPaj6oaZXM2pVMLS
d/8D/QDqFtNHzZYDcQAAAABJRU5ErkJggg==
)
}是等差数列;
(III)已知b
n=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAqCAYAAABLGYAnAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,求数列{a
nb
n}的前n项和S
n.
相关试题
-
已知函数
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAAjCAYAAAB1nT9JAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
(1)求
;
(2)已知数列{an}满足a1=2,an+1=F(an),求数列{an}的通项公式;
(3) 求证:a1a2a3…an>
.
-
已知函数
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAAjCAYAAAB1nT9JAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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=
)
(1)求
;
(2)已知数列{an}满足a1=2,an+1=F(an),求数列{an}的通项公式;
(3) 求证:a1a2a3…an>
.
-
已知函数
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAAjCAYAAAB1nT9JAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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=
)
(1)求
;
(2)已知数列{an}满足a1=2,an+1=F(an),求数列{an}的通项公式;
(3) 求证:a1a2a3…an>
.
-
已知函数
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAAjCAYAAAB1nT9JAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
(1)求
;
(2)已知数列{an}满足a1=2,an+1=F(an),求数列{an}的通项公式;
(3) 求证:a1a2a3…an>
.
-
已知函数
的反函数为f-1(x).设数列{an}满足a1=1,an+1=f-1(an)(n∈N*).
(1)求数列{an}的通项公式;
(2)已知数列{bn}满足
,求证:对一切正整数n≥1都有
…
.
-
已知函数
.设数列{an}满足a1=1,an+1=f(an)(n∈N+).
(1)求数列{an}的通项公式;
(2)已知数列{bn}满足
,
,求证:对一切正整数n≥1都有
<2.
-
已知函数
.设数列{an}满足a1=1,an+1=f(an)(n∈N+).
(1)求数列{an}的通项公式;
(2)已知数列{bn}满足
,
,求证:对一切正整数n≥1都有
<2.
-
已知函数
.设数列{an}满足a1=1,an+1=f(an)(n∈N+).
(1)求数列{an}的通项公式;
(2)已知数列{bn}满足
,
,求证:对一切正整数n≥1都有
<2.
-
已知函数
.设数列{an}满足a1=1,an+1=f(an)(n∈N+).
(1)求数列{an}的通项公式;
(2)已知数列{bn}满足
,
,求证:对一切正整数n≥1都有
<2.
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已知函数
,数列{an}满足a1=1,an+1=f(an)(n∈N+).
(1)求数列{an}的通项公式an;
(2)若数列{bn}满足
,求Sn.