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Thread: Another infinite sequence

  1. #1
    Senior Member mollymcf2009's Avatar
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    Another infinite sequence

    Last one I'm stuck on:

    $\displaystyle a_n$ = ?

    { $\displaystyle 1, -\frac{2}{3}, .4444444444444444, - .296296296296296296,.....$}
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Last one I'm stuck on:

    $\displaystyle a_n$ = ?

    { $\displaystyle 1, -\frac{2}{3}, .4444444444444444, - .296296296296296296,.....$}

    $\displaystyle (-2/3)^n$ where n=0,1,2,...

    or

    $\displaystyle (-2/3)^{n-1}$ where n=1,2,3...
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by matheagle View Post
    $\displaystyle (-2/3)^n$ where n=0,1,2,...

    or

    $\displaystyle (-2/3)^{n-1}$ where n=1,2,3...
    Can you explain this for the fourth term its not coming correctly

    EDIT: It came thanks
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Last one I'm stuck on:

    $\displaystyle a_n$ = ?

    { $\displaystyle 1, -\frac{2}{3}, .4444444444444444, - .296296296296296296,.....$}
    Here is the explanation about third and 4th term

    $\displaystyle x = .4444444444444444.. ---> (1)$

    $\displaystyle 10x = 4.44444...----->(2)$

    (2) - (1)

    $\displaystyle 9x= 4 $

    $\displaystyle
    x = \frac{4}{9} = \frac{ 2\times 2}{ 3 \times 3} $

    $\displaystyle x = -0.296296296296296296 ..---> (1) $

    $\displaystyle 1000x =- 296.296296......----> (2)$

    (2)-(1)

    $\displaystyle 999x = -296 $

    $\displaystyle x = \frac{-296}{999} = \frac{4 \times \not 37 \times -2}{9 \times \not 37 \times 3 }$
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  5. #5
    MHF Contributor matheagle's Avatar
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    That's way too much work 4 me.
    I just used my calculator to check (2/3) to the third power.
    The first three are obvious.
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