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Math Help - sequences and series

  1. #1
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    sequences and series

    We define a sequence recursively in the following way:
    s1=2 and sn=3+2sn−1 for n1
    1. Show that sn is an increasing sequence,
    2. Show that sn is bounded from above,
    3. Compute limnsn
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  2. #2
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    1.3+(2sn)−1 < 3+2(sn+1)−1
    3+2sn-1 < 3+2sn+1
    increasing for all values n

    2... i don't believe it is bounded from above,

    A squence (Sn) is bounded above if there is a number M such that
    Sn<= M for all n>=1 as this is continues to increase there's no M.

    A squence (Sn) is bounded below if there is a number M such that
    M<= Sn for all n>=1 this however is true. it is bounded below. M<2

    3. limnsn of 3+2sn-1

    3+2-1=
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  3. #3
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    Quote Originally Posted by Ashley87 View Post
    We define a sequence recursively in the following way:

    s1=2 and sn=3+2sn−1 for n1
    1. Show that sn is an increasing sequence,
    2. Show that sn is bounded from above,
    3. Compute limnsn
    You have s_n = \sqrt{3 + 2 s_{n-1}}.

    1. and 2. should be OK (say so if that's not the case).

    For 3. you know that a limit exists since the sequence is increasing and bounded above. Assume the limiting value is L. Then s_n \rightarrow L \Rightarrow s_{n-1} \rightarrow L. So L = \sqrt{3 + 2L} \Rightarrow L^2 = 3 + 2L \, ....
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  4. #4
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    Quote Originally Posted by steven_smith View Post
    A squence (Sn) is bounded above if there is a number M such that
    Sn<= M for all n>=1 as this is continues to increase there's no M.
    You are claiming an increasing sequence cannot be bounded above, unfortunatly this is not true. Not only is it not true in general it is not true in this case.

    CB
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by steven_smith View Post
    1.3+(2sn)−1 < 3+2(sn+1)−1
    3+2sn-1 < 3+2sn+1
    increasing for all values n
    Due to limitations with his notation you have the wrong end of the stick about what the OP is asking.

    The intended recurrence is that given in MrF's post.

    CB

    (If you continue responding inappropriatly to posts that you obviously have limmited understanding of I will start issuing infractions, and if I get fed up with that I will just ban you to save tha agravation)
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