(本小題滿分14分)
各項均為正數(shù)的數(shù)列
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,
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,且對滿足

的正整數(shù)

都有

。
(1)當
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時,求通項

;
(2)證明:對任意

,存在與
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有關的常數(shù)

,使得對于每個正整數(shù)

,都有

。
(1)

(2)證明見解析。
(1)由

得

,將

代入化簡得

。
所以

,
故數(shù)列

為等比數(shù)列,從而

,即

。
可驗證,

滿足題設條件。
(2)由題設

的值僅與

有關,記為

則

。
考察函數(shù)

,則在定義域上有
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故對

,

恒成立。
又

,
注意到

,解上式得

,
取

,即有

。
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
,
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
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
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
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
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
;
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
:

(其中

為自然對數(shù)的底數(shù))在點

處的切線與

軸交于點

,過點

作

軸的垂線交曲線

于點

,曲線

在點

處的切線與

軸交于點

,過點

作

軸的垂線交曲線


于點

,……,依次下去得到一系列點

、

、……、

,設點

的坐標為

(

).(Ⅰ)分別求

與

的表達式;(Ⅱ)設
O為坐標原點,求

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數(shù)列

滿足

="1,"

=

,且

(
n≥2),
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則
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等于( )
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