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Thread: Sequence

  1. #1
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    Sequence

    Not sure if how i got to the answer is right
    the question is... is this sequence strictly increasing or strictly decreasing
    $\displaystyle \frac{5^{n}}{2^{n^2}}$sequence with n=1 to infinity
    used $\displaystyle A_{n+1}-A_{n}$
    which gave me $\displaystyle \frac{5^{n+1}}{2^{(n+1)^{2}}}*\frac{2^{n^2}}{5^n}$
    Does simplifying that give me
    $\displaystyle \frac{5}{2^{2n+1}}$which is<1; for n is greater than or equal to 1
    so the sequence is decreasing
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  2. #2
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    Quote Originally Posted by vinson24 View Post
    Not sure if how i got to the answer is right
    the question is... is this sequence strictly increasing or strictly decreasing
    $\displaystyle \frac{5^{n}}{2^{n^2}}$sequence with n=1 to infinity
    used $\displaystyle A_{n+1}-A_{n}$
    which gave me $\displaystyle \frac{5^{n+1}}{2^{(n+1)^{2}}}*\frac{2^{n^2}}{5^n}$


    You must have meant that you put $\displaystyle A_n:=\frac{5^n}{2^{n^2}}$ , and then you did $\displaystyle \frac{A_{n+1}}{A_n}$ , not $\displaystyle A_{n+1}-A_n$ ...

    Does simplifying that give me
    $\displaystyle \frac{5}{2^{2n+1}}$which is<1; for n is greater than or equal to 1
    so the sequence is decreasing

    Indeed.

    Tonio
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  3. #3
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    oops sorry about that thanks
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