Question

(1)2+(2)2+(3)2+...+(n-1)2 =?​

Answer 1

1² + 2² + 3² + .... + (n - 1)²

Applying the summation formula

$\sf \Sigma n^2 = \frac{n(n + 1)(2n + 1)}{6}$

So, for (n - 1) terms,

$\sf sum = \frac{(n - 1)(n - 1 + 1)(2n - 2 + 1)}{6}$

$\sf sum = \frac{n(n - 1)(2n - 1)}{6}$