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$$1^2 + 2^2 + 3^2 ... + n^2$$

Is this a series? or can it be converted to a series? What's its name? Is there a formula? ($F_n$?)

Thanks. (I'm pretty novice when it comes to mathematical notation btw)

Context: I saw a question where you were presented with a square grid, and asked how many squares you could make (this includes each grid cell, but also the whole grid is a square shape, and then there are bigger squares made up of multiple grid cells etc). I figured out that the answer follows the pattern above, and was looking for a full general solution for any grid size.

matt
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The sum $$ 1^2 + 2^2 + 3^2 ... + n^2 = \sum_{k=1}^{n} k^2 $$ is called the sum of the first $n$ squares. There is a formula for this given by $$ \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6} $$ as is shown in the answers to this question.

Robert Lee
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They are the Square Pyramidal numbers.

https://en.m.wikipedia.org/wiki/Square_pyramidal_number

https://mathworld.wolfram.com/SquarePyramidalNumber.html

Neil W
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