Finding an Expression for the Sum of Fourth Powers

A level students will encounter the expressions for the sums of powers of integers, often using mathematical induction to prove their validity, but I don’t remember students ever being asked to investigate and derive those expressions.

This note shows how the sum of fourth powers of integers can be derived and understood by A-level, or younger students. It must be understood that this method does not prove the validity of the expression obtained, but it will allow readers to understand how the expression can be derived.