The sum of first n natural numbers is given by the expression n²/2 + n/2. Factorise this expression.

Solution:

Given, the sum of first n natural numbers is given by the expression n²/2 + n/2

⇒ n²/2 + n/2

= n/2(n + 1)

Note: 'Factor' is a term used to express a number as a product of any two numbers. Factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

For example, (3x²+ 6x)

⇒ 3x(x + 2).

When we multiply (3x) and (x+2), we get the original expression (3x²+ 6x).

✦ Try This: If the sum of the squares of the first ‘n’ natural number is (2n³ + 3n² + n)/6 if one its factor is (2n + 1). Find the remaining factors.

Given, sum of the squares of the first ‘n’ natural number is (2n³ + 3n² + n)/6

(2n³ + 3n² + n)/6 = n(2n² + 3n + 1)/6 = (n)(n + 1)(2n + 1)/6

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 102

The sum of first n natural numbers is given by the expression n²/2 + n/2. Factorise this expression.

Summary:

The sum of first n natural numbers is given by the expression n²/2 + n/2. Factorizing we get, n/2(n + 1)

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