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Math Help - Sigma notation help

  1. #1
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    Question Sigma notation help

    write the sigma notation of (16/81) , (8/27) , (4/9) , ....
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  2. #2
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    Note that 16/2=8, 8/2=4, ..., and 81/3=27, 27/3=9, ..., (the terms are in a geometric progression) so the nth term may be written a_n=\frac{16}{2^{n-1}}\frac{3^{n-1}}{81}=\frac{16}{81}\left(\frac32\right)^{n-1}.

    Edit: im sorry, that would make your sum \sum_{n=0}^\infty\frac{16}{81}\left(\frac32\right)  ^n. i hope that helps.
    Last edited by yyyyy; January 4th 2009 at 08:35 PM. Reason: addition
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  3. #3
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    i was lookin through that and that seem correct

    thanks a bunch
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  4. #4
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    Hello, lucifer_x!

    Write the sigma notation of (16/81) , (8/27) , (4/9) , ....

    "Sigma notation" means that the terms are to be added.


    So we have: . \frac{2^4}{3^4} + \frac{2^3}{3^3} + \frac{2^2}{3^2} + \hdots \;=\;\left(\frac{2}{3}\right)^4 + \left(\frac{2}{3}\right)^3 + \left(\frac{2}{3}\right)^2 + \hdots


    Therefore: . \sum^{\infty}_{n=1} \left(\frac{2}{3}\right)^{5-n}

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  5. #5
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    oh ya my mind totally blanked cuz i have to turn this in so i was kinda rushing thorugh and scaning through it

    u made it so easy to understand , thanks Soroban

    when the test comes around i will know what to do
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