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Maths-

General

Easy

Question

Complete the conjecture. The sum of the first n odd positive integers is ____.

hint Hint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

The correct answer is: Hence, the sum of the first n odd positive integers is n2

Sum of first 3 positive integers = 1 + 3 + 5 = 9 = 3²
Sum of first 4 positive integers = 1 + 3 + 5 + 7= 16 = 4²
Sum of first 5 positive integers = 1 + 3 + 5 + 7 + 9 = 25 = 5²
Sum of first 6 positive integers = 1 + 3 + 5 + 7 + 9 + 11 = 36 = 6²
We can observe that the sum of the first n odd positive integers is n².
Final Answer:
Hence, the sum of the first n odd positive integers is n²

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