Maths-

General

Easy

Question

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

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 = 3^{2}

Sum of first 4 positive integers = 1 + 3 + 5 + 7= 16 = 4^{2}

Sum of first 5 positive integers = 1 + 3 + 5 + 7 + 9 = 25 = 5^{2}

Sum of first 6 positive integers = 1 + 3 + 5 + 7 + 9 + 11 = 36 = 6^{2}

We can observe that the sum of the first n odd positive integers is n^{2}.

Final Answer:

Hence, the sum of the first n odd positive integers is n^{2}

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