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Sum Formula

  1. Oct 3, 2004 #1
    What is the sum formula for this expression??

    "The sum from n=1 to k of (n^c) for any real constant c"

    sigma (n^c)

    (lower limit n=1, upper limit k) for the sum (n^c), where c is any real constant

    Attached Files:

  2. jcsd
  3. Oct 4, 2004 #2
    Sorry, um, the text file needed mathtype to view :frown:

    Um, here's a GIF gif picture format; i attached it and it will open easily (gif picture format) it's an attachment, the GIF image format formula; it will open easily i hope :surprised (whtisthsum.gif)

    Attached Files:

  4. Oct 4, 2004 #3
    Well it would be (c+1)th degree equation in k
    so u can write it as a_(c+1)1*k^(c+1)+a_ck^c+...+a_0

    I am not sure whether there is a neat closed form expression which will give u the a_i's ...

    -- AI
  5. Oct 4, 2004 #4


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  6. Oct 4, 2004 #5
    Yeah, but the n changes, whereas the 'c' stays constant...
    it's not to the power of 1, then 2, then 3...but always to an unchanging constant c...only the 'n' changes as u add...

    1+(2^c)+(3^c)+(4^c)+(5^c)+(6^c)+...+(k^c)...so the c can be any real value...but c remains constant!! only the 'n' changes!<=as u add

    That's why this is not really a power series,; the 'c' must be constant, and cannot change! (that's why the [tex]\frac{x}{1 - x}[/tex] doesn't work)!
    Last edited: Oct 4, 2004
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