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Thread: [SOLVED] Sequence problem

  1. #1
    Senior Member mollymcf2009's Avatar
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    [SOLVED] Sequence problem

    I've tried about 100 different scenarios and can't seem to get this one:

    Find a formula for the general term $\displaystyle a_n$ of the sequence, assuming the pattern of the first few terms continues:

    { $\displaystyle \frac{1}{4}, \frac{2}{9}, \frac{3}{16}, \frac{4}{25}, ...$ }


    $\displaystyle a_n$ = ?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    I've tried about 100 different scenarios and can't seem to get this one:

    Find a formula for the general term $\displaystyle a_n$ of the sequence, assuming the pattern of the first few terms continues:

    { $\displaystyle \frac{1}{4}, \frac{2}{9}, \frac{3}{16}, \frac{4}{25}, ...$ }


    $\displaystyle a_n$ = ?
    Hint: The sequence can be written as $\displaystyle \left\lbrace\frac{1}{2^2},\frac{2}{3^2},\frac{3}{4 ^2},\frac{4}{5^2},\dots\right\rbrace$

    Can you try to come up with an expression for $\displaystyle a_n$ now?
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  3. #3
    Senior Member mollymcf2009's Avatar
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    $\displaystyle \frac{n}{(n+1)^2}$

    Thanks Chris!!
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