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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Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2, 4, 7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
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