Question

2. Which of the following can be the square of a natural number 'n'?
(1) sum of the squares of first n natural numbers
(ii) sum of the first n natural numbers
(iii) sum of first (n - 1) natural numbers
(iv) sum of first 'n' odd natural numbers.
​

Answer 1

Answer:

(iv) sum of first 'n' odd natural numbers.

Step-by-step explanation:

1+3  (2 terms) = 4 = 2²

1+3+5 (3 terms) = 9 = 3²

1+3+5 +7  (4 terms) = 16 = 4²

1+3+5+7+9 (5 terms) = 25 = 5²

=> 1+3+5+... 'n'terms = n²

ie., sum of first 'n' odd natural numbers =  n²