The sum of the first n odd natural numbers is n². State whether the statement is true or false.
Solution:
Given, the sum of first n odd natural numbers is n².
We have to determine if the given statement is true or false.
Natural numbers are a part of the number system, including all the positive integers from 1 to infinity.
Natural numbers are also called counting numbers because they do not include zero or negative numbers.
Odd numbers definition is given as those numbers which cannot be divided into two parts equally.
We know that the sum of first n odd natural numbers is given by n².
Example: Consider 1, 3, 5, 7, 9, 11, 13, 15, 17.
Here, n = 9
n² = 9² = 81
Sum of successive odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17
= 25 + 24 + 32
= 49 + 32
= 81
Therefore, the given statement is true.
✦ Try This: The sum of the first n odd natural numbers is 4n. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 62
The sum of the first n odd natural numbers is n². State whether the statement is true or false
Summary:
The given statement, ”The sum of the first n odd natural numbers is n²” is true.
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