# Further Maths - Sums of Squares

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/sums-of-squares/ · Updated: 2020-09-16 · Tags: further-maths, series, school

##### What is the formula for the sum of the squares of the $n$ natural numbers??
$$
\sum^{n}_{r=1} r^2 = \frac{1}{6}n(n+1)(2n+1)
$$

##### How could you rewrite $\sum^{n}_{r=1} r^2$??
$$
\frac{1}{6}n(n+1)(2n+1)
$$

##### What's another way of expressing $\frac{1}{6}n(n+1)(2n+1)$??
$$
\sum^{n}_{r=1} r^2
$$

##### How could you rewrite $\sum^{n}_{r=1} 3r^2$??
$$
\frac{1}{3}n(n+1)(2n+1)
$$

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