Power Sum and Sum of Partial Power Sums

(May 1, 2008)

 

Power Sum

 

     

      where p, n are positive integers.

 

 

The computation of Power Sum for p = 1, 2, …, 14 gives

 

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12. 

 

      

 

 

                       

 

13. 

      

 

 

 

 

14. 

       

 

 

 

 

Sum of Partial Power Sum (Update of Repeated Power Series, June 27, 2005)

 

Define

,

where m, n, k, and i are positive integers.

 

 

The computation of following identifies for m = 1, 2, …, 12 is true for all positive n.

 

1.     

 

2.     

 

 

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12. 

 

 

 

 

 

(May 1, 2008)

 

Similar series existed for Finite Alternative Odd Power Series.

 

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