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JAMB Geography 2022 Paper

Question : 13

Total: 40

Which of the following is an importance of the atmosphere to living organisms?

Solution:

Let

n

be a natural number.

Consider the expression:

n^2+n+3 = n(n+1)+3

The product

n(n+1)

is the product of two consecutive integers.

For any two consecutive integers, one of them must be even. Therefore, their product has a factor of

2

, so:

n(n+1) \text{ is even}

Since an even number plus

3

is always odd, it follows that:

n(n+1)+3 \text{ is odd}

Thus:

n^2+n+3 \text{ is odd}

So the claim is true for every natural number

n

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