(本題滿分18分)本題共有3個(gè)小題,第1小題滿分4分,第2小題滿分6分,
第3小題滿分8分.
已知數(shù)列
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:
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,
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,
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,
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(
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是正整數(shù)),與數(shù)列
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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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是正整數(shù)).記
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.
(1)若
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,求
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的值;
(2)求證:當(dāng)
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是正整數(shù)時(shí),
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;
(3)已知
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,且存在正整數(shù)
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,使得在
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,
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,
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,
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中有4項(xiàng)為100.
求
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的值,并指出哪4項(xiàng)為100.
(1)4
(2)證明見解析.
(3)
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(1)
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
………………..2分
∵
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………………..4分
(2)證明:用數(shù)學(xué)歸納法證明:當(dāng)
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① 當(dāng)n=1時(shí),
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等式成立….6分
② 假設(shè)n=k時(shí)等式成立,即
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那么當(dāng)
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時(shí),

………8分
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等式也成立.
根據(jù)①和②可以斷定:當(dāng)
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…………………...10分
(3)
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………………………..13分
∵ 4m+1是奇數(shù),
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均為負(fù)數(shù),
∴這些項(xiàng)均不可能取到100. ………………………..15分
此時(shí),
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為100. …………………18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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
,且


.
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
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
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
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已知數(shù)列

,

,

,

,

,…,這個(gè)數(shù)列的特點(diǎn)是從第二項(xiàng)起,每一項(xiàng)都等于它的前后兩項(xiàng)之和,則這個(gè)數(shù)列的前

項(xiàng)之和

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已知等差數(shù)列的前
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項(xiàng)和為
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,前
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項(xiàng)和為
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,求前
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項(xiàng)和.
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