- #1
ehrenfest
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Homework Statement
I encountered this formula in a proof:
Let [tex]S_k(n)[/tex] be the sum of the first n positive integers raised to the power of k:
e.g. [tex]S_3(5) = 1^3 + 2^3+3^3+4^3+5^3[/tex]
How would one show that
[tex]S_2(n) = (n^3/3) + (n^2/2) + an[/tex]
and that
[tex]S_4(n) = (n^5/5) + (n^4/2) +bn^3 + cn^2 +dn [/tex]
where a,b,c,d are constants.