設(shè)等差數(shù)列
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的前
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項(xiàng)和為
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,公比是正數(shù)的等比數(shù)列
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的前
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項(xiàng)和為
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,已知
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(1)求
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的通項(xiàng)公式。
(2)若數(shù)列
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滿足
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求數(shù)列
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的前
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項(xiàng)和
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。
(1)由等差數(shù)列和等比數(shù)列的通項(xiàng)公式與求和公式可分別求出公差和公比,即可寫出
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的通項(xiàng)公式;(2)令
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,寫出與
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類似的式子,兩式相減求出
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的通項(xiàng)公式,注意分段表示,再由等差數(shù)列的求和公式得
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的前
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項(xiàng)和
⑴ 設(shè)等差數(shù)列
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的公差為
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,等比數(shù)列
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的公比為
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由
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,得
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①
由
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得
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②
化簡(jiǎn)①②
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消去
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得
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
或
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則
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(7分)
⑵
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…
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①
當(dāng)
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時(shí),
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…
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②
由①-②得
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又由⑴得
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的前
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項(xiàng)和
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…
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分14分)
在數(shù)列
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中,

,且前
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項(xiàng)的算術(shù)平均數(shù)等于第

項(xiàng)的

倍(
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). (即

(1)寫出此數(shù)列的前5項(xiàng);
(2)歸納猜想

的通項(xiàng)公式,并加以證明.
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科目:高中數(shù)學(xué)
來源:不詳
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(本小題滿分14分)已知數(shù)列{an}是以d為公差的等差數(shù)列,數(shù)列{bn}是以q為公比的等比數(shù)列
(Ⅰ)若數(shù)列{bn}的前n項(xiàng)和為Sn,且a1=b1=d=2,S3<5b2+a88-180,求整數(shù)q的值
(Ⅱ)在(Ⅰ)的條件下,試問數(shù)列{bn}中是否存在一項(xiàng)bk,使得b,k恰好可以表示為該數(shù)列中連續(xù)P(P∈N,P≥2)項(xiàng)和?請(qǐng)說明理由。
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科目:高中數(shù)學(xué)
來源:不詳
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已知函數(shù)

,數(shù)列

滿足

.
(1)證明數(shù)列

是等差數(shù)列,并求數(shù)列

的通項(xiàng)公式;
(2)記

,求
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分16分)
數(shù)列

的前n項(xiàng)和為

,存在常數(shù)A,B,C,使得

對(duì)任意正整數(shù)n都成立。
(1) 若數(shù)列

為等差數(shù)列,求證:3A-B+C=0;
(2) 若
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設(shè)
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數(shù)列
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的前n項(xiàng)和為

,求
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;
(3) 若C=0,

是首項(xiàng)為1的等差數(shù)列,設(shè)

,求不超過P的最大整數(shù)的值。
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
已知數(shù)列
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滿足

.若

,則

_____________.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分12分)
已知正數(shù)數(shù)列

的前n項(xiàng)和為

,且

,數(shù)列

滿足
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(Ⅰ)求數(shù)列

的通項(xiàng)公式與

的前n項(xiàng)和

;
(Ⅱ)設(shè)數(shù)列

的前項(xiàng)和為
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,求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
求
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=
.
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