Sums of Powers of Integers

An Exploration Using Summations

In this exploration we want to look at one means for deriving the formula for each of the following:

We will be using a particular strategy/technique: examining the formula for the next higher power. What follows is more of providing the derivations than in posing questions. I suggest the reader may benefit from rephrasing the derivations using their own notation.

S1

S2

S3