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GeoMike

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I was reading through a proof of the summation formula for a sequence of consecutive squares (1

(k+1)

And take "k = 1,2,3,...,n-1, n" to get

I can follow the proof without issue, what I'm a little confused about is where "(k+1)

Hopefully what I'm asking makes sense...

-GeoMike-

^{2}2^{2}+ 3^{2}+ ... + n^{2}), and the beginning of the proof states that we should take the formula:(k+1)

^{3}= k^{3}+ 3k^{2}+ 3k + 1And take "k = 1,2,3,...,n-1, n" to get

**n**formulas which can then be manipulated into the form n(n+1)(2n+1)/6I can follow the proof without issue, what I'm a little confused about is where "(k+1)

^{3}= k^{3}+ 3k^{2}+ 3k + 1" comes from. It's just given at the beginning of the proof with no logical explanation as to where it came from. I understand that using it allows us to easily get to the final form -- but is there some logical connection between the cubed binomial (and it's expansion) and the sum of the sequence of squares?Hopefully what I'm asking makes sense...

-GeoMike-

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