Question

1² +2²+3² +...+ (n − 1)² =​

Answer 1

The sum of number squares can be worked out using the formula

Σn = (2 x n ^3 + 3 x n ^ 2 + n)/6

So for sum of n = 1, Σn = (2 x 1^3 + 3 x 1 ^2 + 1) / 6 = 6 /6 = 1

Using this formula, I will work out the sum of all numbers up to 10.

n = 1 , Σn = 1

n = 2, Σn = 5

n = 3, Σn = 14

n = 4, Σn =30

n = 5, Σn = 55

n = 6, Σn = 91

n = 7, Σn = 140

n = 8, Σn = 204

n = 9, Σn = 285

n = 10, Σn = 385

Answer 2

The sum of number squares can be worked out using the formula

Σn = (2 x n ^3 + 3 x n ^ 2 + n)/6

So for sum of n = 1, Σn = (2 x 1^3 + 3 x 1 ^2 + 1) / 6 = 6 /6 = 1

Using this formula, I will work out the sum of all numbers up to 10.

n = 1 , Σn = 1

n = 2, Σn = 5

n = 3, Σn = 14

n = 4, Σn =30

n = 5, Σn = 55

n = 6, Σn = 91

n = 7, Σn = 140

n = 8, Σn = 204

n = 9, Σn = 285

n = 10, Σn = 385