若數(shù)列
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滿(mǎn)足
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(其中d為常數(shù),
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),則稱(chēng)數(shù)列
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為“調(diào)和數(shù)列”,已知數(shù)列
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為調(diào)和數(shù)列,且
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,則
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的最大值為
.
試題分析:因?yàn)閿?shù)列
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為“調(diào)和數(shù)列”,所以x
n+1-x
n=d(n∈N
*,d為常數(shù)),即數(shù)列{x
n}為等差數(shù)列,由x
1+x
2+…+x
20=200得
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即
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,
易知x
3、x
18都為正數(shù)時(shí),x
3x
18取得最大值,所以
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,即
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的最大值為100.
點(diǎn)評(píng):解本小題關(guān)鍵是根據(jù)因?yàn)閿?shù)列
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為“調(diào)和數(shù)列”,得到{x
n}為等差數(shù)列,然后再解題的過(guò)程中利用性質(zhì):若
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,則
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,得到
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,然后使用基本不等式求出
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的最值.
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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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
=1,且

=

+

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的前
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
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
,

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,使得對(duì)一切正整數(shù)
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,
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都成立,則
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的最小值是________.
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來(lái)源:不詳
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已知

是首項(xiàng)為

,公差為

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
;
(2)設(shè)

是首項(xiàng)為
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,公比為

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
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項(xiàng)和

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