Square Sum

Number Theory Level 1

Evaluate

$1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 .$

1 solution

Arron Kau Staff
May 13, 2014

By the sum of squares formula,

$\sum_{i=1}^n i^2 = \frac{ n (n+1)(2n+1)} { 6}$

Thus, the sum of the first 9 squares is equal to $\frac{ 9 \times 10 \times 19} { 6} = 285$ .

Note: We may also expand out each term and add manually.