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(本小题满分14分)
已知数列是首项为,公差为的等差数列,是首项为,公比为的等比数列,且满足,其中.
(Ⅰ)求的值;
(Ⅱ)若数列与数列有公共项,将所有公共项按原顺序排列后构成一个新数列,求数列的通项公式;
(Ⅲ)记(Ⅱ)中数列的前项之和为,求证:
.
解:(Ⅰ)由题设.  ………1分
由已知,所以.又b>0,所以a<3. …2分
因为,则.又a>0,所以b>2,从而有.   …3分
因为,故.          …………………4分
(Ⅱ)设,即.   ………………5分
因为,则,所以.  ………………6分
因为,且b∈N*,所以,即,且b=3. ……7分
.        …………………8分
(Ⅲ)由题设,.  …………………9分
时,,当且仅当时等号成立,所以.   ……………11分
于是.  12分
因为S1=3,S2=9,S3=21,则

.  …………………14分解析:
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