Sum of the fourth powers of the first n positive integers

[AGMS]

Homework Statement

Find a formula fo the sum of the fourth powers of the first n positive integers

n
∑ i^4
(i=1)


Justify your work using mathematical induction

Homework Equations

so i know the formula for the sum of the cubes of the first n positive integers

k=n+1
∑ = (1^3)+(2^3)+(3^3)+...+(n^3)+((n+1)^3)= {((n+1)^2)((n+2)^2)} / (4)
k=1

I was wondering what was the proof for the sum of the quartic of the first n positive integers

The Attempt at a Solution

This is actually what I started working out and I don't know whether it is right

N
∑ i^4 = (1/30)(N+1)(N)(2N+1)((3N^2)+3N-1)
i=1

 

[Dick]

Sure, that's right. I know it's right because I looked it up. Just like you, probably. The problem is that you have to prove it's right. Call your sum S(N). Then the inductive step (after you shown it's true for N=1) is to show S(N+1)-S(N)=(N+1)^4. Do you see why? If you see why, that's the important part.