Question 62

State whether the following statement is true or false:

The sum of first n odd natural numbers is $n^{2}$ .

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Solution

True
Sum of odd natural numbers $= \sum (2 n - 1) = \frac{2 \times n \times (n + 1)}{2} - n$
$= n^{2} + n - n = n^{2}$

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The sum of three odd numbers is even.

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State whether the following statement is true or false:

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n

\frac{n^{2} - 1}{4}

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