(本小題滿分10分)
已知各項(xiàng)均為正數(shù)的數(shù)列{
an}前n項(xiàng)和為S
n,

=2,且2,
an,S
n成等差數(shù)列。
(1)求數(shù)列{
an}的通項(xiàng)公式;
(2)若

,求數(shù)列{

}的前n項(xiàng)和T
n;
(3)記數(shù)列

的前n項(xiàng)和為

,求證:

.
(1)

(2)

(3)略
解:(1)由題意知
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,
當(dāng)n≥2時,

,

,
兩式相減得

整理得:
∴數(shù)列{

}是以2為首項(xiàng),2為公比的等比數(shù)列。
∴

……4分
(2)由(1)知

,所以

, …………①

, …………②
①-②得

,
∴

, ∴

, ……7分
(3)

數(shù)列

是首項(xiàng),公比均為1/4的等比數(shù)列

……10分
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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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
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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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