(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sum of the first n powers

**Physics Forums | Science Articles, Homework Help, Discussion**