How to calculate the sum of squares?
Below are the formulas for sum of squares:
Formula 1: For addition of squares of any two numbers a and b is represented by:
a2+ b2 = (a + b)2 – 2ab
where a and b are real numbers
As per algebraic identities, we know;
(a + b)2 = a2 + b2 + 2ab
Therefore, we can write the above equation as;
a2+b2 = (a + b)2 – 2ab
Formula 2: For squares of any three numbers say a, b, and c is represented by:
a2 + b2 + c2 = (a + b + c)2 – 2ab – 2bc – 2ac
where a, b and c are real numbers
From the algebraic identities, we know;
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
Therefore, we can write the above equation as;
a2 + b2 + c2 = (a + b + c)2 – 2ab – 2bc – 2ac
Formula 3: For nth Natural Numbers
The natural numbers include all the counting numbers, starting from 1 till infinity. If nth consecutive natural numbers are 1, 2, 3, 4, …, n, then the sum of squared ‘n’ consecutive natural numbers is represented by 12 + 22 + 32 + … + n2.
it is also denoted by the notation Σn2. The formula for the addition of squares of natural numbers is given below:
Σn2 = [n(n + 1)(2n + 1)]/6
Formula 4: Sum of Squares of First n Odd Numbers
The addition of squares of first odd natural numbers is represented by:
Σ(2n – 1)2 = [n(2n + 1)(2n – 1)]/3
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