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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Question 2 (a)

State whether the following statement is true or false:

The sum of three odd numbers is even.

Question 2 (c)

State whether the following statement is true or false:

The product of three odd numbers is odd.

Question 58

State whether the following statement is true or false:

The square of every natural number is always greater than the number itself.

Question 72

State whether the following statement is true or false:

The square root of a perfect square of n digits will have $(\frac{n + 1}{2})$ digits, if n is odd.

$1 + 3 + 5 + . . . . . + (2 n - 1) = n^{2}$ i.e., the sum of first n odd natural numbers is $n^{2}$ .

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