In this video I show the proof for determining the formula for the sum of the squares of "n" consecutive integers, i.e. 1² + 2² + 3² +.... + n². This is a pretty abstract proof and makes use of the useful "telescoping" or collapsing sum which I illustrate in the video. The formula for the sum of squares comes up very often in calculus so it's a good idea to understand the proof!

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Sum of the squares of “n” positive integers

Simple Proof

We start off the proof with the “telescoping sum” (or the collapsing sum):

Example