設數(shù)列
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是首項大于零的等比數(shù)列,則“
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”是“數(shù)列
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是遞增數(shù)列”的( )
A.充分而不必要條件 |
B.必要而不充分條件 |
C.充分必要條件 |
D.既不充分也不必要條件 |
試題分析:若已知
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,則設數(shù)列
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的公比為
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,
因為
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,所以有
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,又
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,解得
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,所以數(shù)列
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是遞增數(shù)列;
反之,若數(shù)列
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是遞增數(shù)列,則公比
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且
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,所以
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,即
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,
所以
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是數(shù)列
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是遞增數(shù)列的充分必要條件.故選C.
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