数列
满足
,设
.
(1)判断数列
是等差数列吗?试证明;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdb85421bbe46a578f83483001b291e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687601d7351f1ab75b5c7e22000a7895.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
更新时间:2018-08-12 21:12:33
|
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解答题-证明题
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适中
(0.65)
名校
解题方法
【推荐1】给定数列
,若满足
且
,对于任意的
,都有
,则称数列
为“指数型数列".
(1)已知数列
满足
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是不是“指数型数列"?若是,请给出证明,若不是,请说明理由;
(2)若数列
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,证明:数列
中任意三项都不能构成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3783e69ef5a6a0af566ff4e21ccf03.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66e0c09fde97de0e9d73e6f457a03b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb34b6f01296502fd0f9adf8c78bea6f.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4e5ccd2179d6e7090a9a26122661da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
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解答题-问答题
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【推荐2】在数列
中,
它的前
项和为
对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4fc49df8331a641fdb54fd92035a6d.png)
成等差数列.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db76a64a8e204241312598120bf6978.png)
(2)猜想数列
的通项公式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d963b4c5ad02bb5a8453f5fc923ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117464f527849ab995858aaa20f4175b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4fc49df8331a641fdb54fd92035a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c073674fcbfa8763fe559d2f93ce08d0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db76a64a8e204241312598120bf6978.png)
(2)猜想数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
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解答题-证明题
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【推荐1】已知数列
中,各项均为正数,其前
项和为
,且满足
.
(Ⅰ)求证数列
为等差数列,并求数列
的通项公式;
(Ⅱ)设
,数列
的前
项和为
,若
对所有的
和
都成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03d97969dc165cfec23ef7caed3a297.png)
(Ⅰ)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f725428c3da4cd3d18c67a27be0e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553c4dac28168db7f2dc54570cf78495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37378457fc05673cbfc517c2f9452892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】已知数列
的前
项和为
,
且
,数列
为等差数列,且公差
,
;
求数列
的通项公式;
若
成等比数列,求数列
的前项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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