Power Sum and Sum of Partial Power Sums

Power Sum and Sum of Partial Power Sums
(May 1, 2008)
 
Power Sum
 
     
      where p, n are positive integers.
 
 
Computing the Power Sum for p = 1, 2, …, 14 gives
 
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Sum of Partial Power Sum (Update of Repeated Power Series, June 27, 2005)
 
Define
,
where m, n, k, and i are positive integers.
 
 
Computing the Sum of Partial Power Sum for m = 1, 2, …, 12 and for all positive n gives
 
1.     
 
 
 
2.     
 
 
 
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1.     
 
 
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(May 1, 2008)
 

Similar seriesFinite Alternative Odd Power Series.

In-Text or Website Citation
Tue N. Vu, Power Sum and Sum of Partial Power Sums, 05/01/2008, from Series Math Study Resource.
Hyperlink: http://seriesmathstudy.com/sms/PowerSumandSumofPowerSum.

Numbers are the highest degree of knowledge. It is knowledge itself.  
 Plato