Without adding find the sum(i) 1 + 3 + 5 + 7 + 9(ii) 1 + 3 + 5 + 7 + 9

1.	Without adding find the sum(i) 1 + 3 + 5 + 7 + 9(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Answer» We know that the sum of first n odd natural numbers is n2. (i) Here, we have to find the sum of first five odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 = 5² = 25 (ii) Here, we have to find the sum of first ten odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10² = 100 (iii) Here, we have to find the sum of first twelve odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19 + 21 + 23 = 12² = 144

Without adding find the sum(i) 1 + 3 + 5 + 7 + 9(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Answer»

We know that the sum of first n odd natural numbers is n2.

(i) Here, we have to find the sum of first five odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 = 5² = 25

(ii) Here, we have to find the sum of first ten odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10² = 100

(iii) Here, we have to find the sum of first twelve odd natural numbers. Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19 + 21 + 23 = 12² = 144