What is the sum of $1^4 + 2^4 + 3^4+ \dots + n^4$ and the derivation for that expression What is the sum of $1^4 + 2^4 + 3^4+ \dots + n^4$ and the derivation for that expression using sums $\sum$ and double sums $\sum$$\sum$?

If you don't want to look up Faulhaber's formula you could try $$(n+1)^5-n^5=5n^4+10n^3+10n^2+5n+1$$
If you sum both sides of this, and know how to compute the sums of $n^3, n^2, n \text{ and } 1$ you should be able to work out the sum of $n^4$.
