(本小題滿分12分)已知數(shù)列{
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}滿足
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=
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,
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是{
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}的前
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項(xiàng)的和,
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. (1)求
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;(2)證明:
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(1)S
n=
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(2)略
(1)由題意S
n=
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兩式相減得2a
n+1=(n+1)a
n+1-na
n即(n-1)a
n+1=na
n,
所以
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再相加得
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即
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所以數(shù)列{a
n}是等差數(shù)列. ………………4分
∵a
1=
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∴a
1=0,
又a
2=1,則公差為1,∴a
n=n-1,
所以數(shù)列{a
n}的前n項(xiàng)的和為S
n=
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………………6分
(2)(1+
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………………8分
①當(dāng)n=1時(shí):(1+
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②當(dāng)n≥2時(shí):
∵
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………………10分
∴(1+
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…+
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而(1+
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,∴
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綜上所證:
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………………12分
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科目:高中數(shù)學(xué)
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(本小題滿分12分)
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
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(本小題12分)
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
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
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
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
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,問
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等于數(shù)列

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的前
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項(xiàng)和分別記為
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和
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,
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的最大值為
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,當(dāng)
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時(shí),試比較
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與
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的大小
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項(xiàng)和為
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且滿足:
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
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
,
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
中,

,

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
項(xiàng)和
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
其中(

,

).
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
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為非零整數(shù),

),試確定

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
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
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
,

,

,且項(xiàng)

分別是某一等比數(shù)列

中的第
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項(xiàng),(1)求數(shù)列

的第12項(xiàng); (2)求數(shù)列

的第

項(xiàng)。
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來源:不詳
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在等比數(shù)列

中,

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