等差數(shù)列
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及等比數(shù)列
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中,
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則當
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時有
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科目:高中數(shù)學
來源:不詳
題型:解答題
設數(shù)列{
an}的首項
a1=1,前
n項和
Sn滿足關系式:3
tSn-(2
t+3)
Sn-1=3
t(
t>0,
n=2,3,4…).
(1)求證: 數(shù)列{
an}是等比數(shù)列;
(2)設數(shù)列{
an}的公比為
f(
t),作數(shù)列{
bn},使
b1=1,
bn=
f(
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)(
n=2,3,4…),求數(shù)列{
bn}的通項
bn;
(3)求和:
b1b2-
b2b3+
b3b4-…+
b2n-1b2n-
b2nb2n+1.
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科目:高中數(shù)學
來源:不詳
題型:解答題
設函數(shù)
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的定義域為
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,當
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時,
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,且對任意的實數(shù)
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,有
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.
⑴求
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,判斷并證明函數(shù)
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的單調性;
⑵數(shù)列
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滿足
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,且
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①求
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通項公式;
②當
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時,不等式
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對不小于
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的正整數(shù)恒成立,求
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的取值范圍.
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科目:高中數(shù)學
來源:不詳
題型:解答題
(13分) 已知曲線
C:
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的橫坐標分別為1和
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,且
a1=5,數(shù)列{
xn}滿足
xn+1 =
tf (
xn – 1) + 1(t > 0且
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).設區(qū)間
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,當
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時,曲線
C上存在點
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使得
xn的值與直線
AAn的斜率之半相等.
(1) 證明:
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是等比數(shù)列;
(2) 當
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
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對一切
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恒成立時,求
t的取值范圍;
(3) 記數(shù)列{
an}的前
n項和為
Sn,當
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時,試比較
Sn與
n + 7的大小,并證明你的結論.
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科目:高中數(shù)學
來源:不詳
題型:填空題
若數(shù)列
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的前
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項和
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,則此數(shù)列的通項公式為
數(shù)列
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中數(shù)值最小的項是第
項.
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知數(shù)列
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的首項為
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(1)若
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,求證:數(shù)列
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是等比數(shù)列;(2)若
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,求數(shù)列
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的前
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項和.
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