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Find the sum of series

  1. Sep 8, 2006 #1
    Can anyone teach me how to find the sum of the series in terms of n in the following:

    1+2x3^2+3x3^4+............+(n+1)3^2n

    Thx!
     
  2. jcsd
  3. Sep 8, 2006 #2

    0rthodontist

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    This can be done with generating functions if you know them.
    1. Find the generating function for 1, 3^2, 3^4, ...
    2. From this, find the generating function for 1, 2*3^2, ...
    3. Find the generating function for (n+2)*3^(2(n+1)), (n+3)*3^(2(n+2)), ...
    4. Subtract the latter from the former and evaluate at 1.
     
  4. Sep 8, 2006 #3


    i dont know what generating function is but what i know is to use the summation sign to do this kind of question. i still cant do it.........
     
  5. Sep 8, 2006 #4

    shmoe

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    You might find it easier to try and sum:

    [tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]
     
  6. Sep 8, 2006 #5

    shmoe

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    You might find it easier to try and sum:

    [tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]

    It's not quite a geometric series, but can you turn it into one?
     
  7. Sep 8, 2006 #6

    0rthodontist

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    Okay--what sums can you do that might be relevant?
     
  8. Sep 8, 2006 #7

    i just can do till this step:

    n+1 E(Sigma) r=1 (r*x^(r-1))
     
  9. Sep 8, 2006 #8


    I can do the summation of x, x^2 .....x^n, x(x+1),x(x+1)(x+2).....

    actually this is my first time to touch this kind of math:)
     
  10. Sep 8, 2006 #9

    0rthodontist

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    Well--
    x + x^2 + ... + x^n
    Take the derivative with respect to x, both term-by-term and in the sum you know.
     
    Last edited: Sep 8, 2006
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