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Finding Formula for partial sums of series.

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data
    I have the series 1^3+2^3+3^3......n^3, and need to find a formula containing n to represent the sum of the nth terms. The motivation is to find a conjecture, which I can then prove using mathematical induction.



    3. The attempt at a solution
    I see that

    n=1 , 1^3=1

    n=2 , 1^3+2^3=9

    n=3, 1^3+2^3+3^3=36

    n=4, sum=100
    n=5 sum = 225. But I cannot come up with a formula to represent the sums. I think this is calculus II series material, but I'm not sure where to start. Could someone point me in the right direction? I used a computer to arrive at

    1^3+2^3+3^3......n^3=(1/4)*n^2*(n+1)^2

    but do not understand how to get there myself.
     
  2. jcsd
  3. Feb 19, 2012 #2
    1=1^2

    9 = x^2

    36 = y^2

    100 = z^2

    etc what are x,y,z? notice something?
     
  4. Feb 20, 2012 #3
    Ok.

    n= 1 2 3 4 5
    sum= 1 3^2 6^2 10^2 15^2

    (sum)^1/2= (n/2)*(n+1)

    So [(n/2)*(n+1)]^2.
     
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