Evaluating a sum of squares using the closed-form formula

Identify that the sum $\sum_{k=1}^{10} k^2$ matches the closed-form formula $\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}$ with $n = 10$. Substituting gives $\frac{10(10+1)(2\cdot 10 + 1)}{6} = \frac{10 \cdot 11 \cdot 21}{6}.$

Now compute the numerator: $10 \cdot 11 \cdot 21 = 2310$. Dividing by 6 gives $2310/6 = 385$, so $\sum_{k=1}^{10} k^2 = 385$.