Sum of powers of integers

  • Thread starter eljose
  • Start date
500
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Let,s suppose we want to do this sum:

[tex] 1+2^{m}+3^{m}+............+n^{m} [/tex] n finite

then we could use the property of the differences:

[tex] \sum_{n=0}^{n}(y(k)-y(k-1))=y(n)-y(0) [/tex]


so for any function of the form f(x)=x^{m} m integer you need to solve:

[tex] y(n)-y(n-1)=n^{m} [/tex] i don,t know how to solve

it..:frown: :frown: i have tried the ansatz y(n)=K(n) with K(n) a Polynomial of degree m+1 but i don,t get the usual results for the sum..could someone help?..
 

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