练习册

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    An animal or a plant that is going extinct A. no longer exists in the world B. comes into this world soon C. becomes very dangerous D. has fewer and fewer living members B Once we climbed a very high mountain. It was so challenging for me because I was only ten years old. During the first few hours of climbing . I enjoyed the flowers and trees, and the birds’ singing, but as time passed, I got a pain in both of my legs. I wanted to quit climbing. In fact, I hated it at that mountain, but my father said to me, “You can always see a beautiful sky at the top of the mountain, but you can’t see it before you reach the top. Only there at the top, can you see all of the nice things, just like in life. At that time, I was too young to understand his words. But later after that, I got knew hope and confidence. I found myself standing at the top of the sky, which was as clear as crystal . 【查看更多】

     

    题目列表(包括答案和解析)

    已知正数数列{an}的前n项和为Sn，满足an2=Sn+Sn-1（n≥2），a1=1．
    （I）求证：数列{an}为等差数列，并求出通项公式；
    （II）设bn=（1-an）2-a（1-an），若bn+1＞bn对任意n∈N*恒成立，求实数a的取值范围．

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    已知a＞0，数列{an}满足a1=a，an+1=a+
    1
    an
    ，n=1，2，….
    （I）已知数列{an}极限存在且大于零，求A=
    lim
    n→∞
    an    （将A用a表示）；
    （II）设bn=an-A，n=1，2，…，证明：bn+1=-
    bn
    A(bn+A)
    ；
    （III）若|bn|≤
    1
    2n
    对n=1，2，…    都成立，求a的取值范围．

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    用数学归纳法证明an+1+（a+1）2n-1能被a2+a+1整除（n∈N*）．

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    已知数列{an}的前n项和为Sn=an-1（a为不为零的实数），则此数列（　　）
    A、一定是等差数列B、一定是等比数列C、或是等差数列或是等比数列D、既不可能是等差数列，也不可能是等比数列

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    （2008•深圳二模）已知数列{an}满足a1=a，an+1=
    (4n+6)an+4n+10
    2n+1
    (n∈N*)    ．
    （Ⅰ）试判断数列{
    an+2
    2n+1
    }    是否为等比数列？若不是，请说明理由；若是，试求出通项an．
    （Ⅱ）如果a=1时，数列{an}的前n项和为Sn．试求出Sn，并证明
    1
    S3
    +
    1
    S4
    +…+
    1
    Sn
    ＜
    1
    10
    （n≥3）．

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