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Summation Notation for [(i^3)/(N^3)]

  1. Jan 14, 2013 #1
    I think I get summation notation when when there are more numbers than variables
    6
    Ʃ i/6 <---I can figure that out.
    i=1

    But I'm confused on how to find what this equals:
    N
    Ʃ (i^3)/(N^3) = ?
    i=1

    How do you add something N times? ...I could deal with a number like 6, but I'm confused about N...

    Any help? :/

    Thank you! :)
     
  2. jcsd
  3. Jan 14, 2013 #2

    Mark44

    Staff: Mentor

    The first term in the summation is 1/N3.
    The second term is 8/N3.

    Can you continue?
    What is the last term in the summation?

    You will necessarily need to use an ellipsis (i.e., "..." ) when you expand this summation.
     
  4. Jan 14, 2013 #3
    So the (N)^3 in denominator is just kept as (N)^3!

    Okay, would this be the answer then:

    1/(N^3) + 8/(N^3) + 27/(N^3) + ... + ((N-1)^3)/(N^3) + (N^3)/(N^3)
     
  5. Jan 14, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, if that's the form you want the answer in. If you actually want to sum it up there is a formula for 1^3+2^3+3^3+...+N^3. Just like there is a formula for 1+2+3+...+N=(N+1)N/2. Probably easiest to try and look it up unless you are required to prove it.
     
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