Question

Without adding, find the sum of the following numbers 

(i) 1 + 3 + 5 + 7 + 9 = 

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 =

Answer 1

(i) 1 + 3 + 5 + 7 + 9 = (5)² = 5 x 5 = 25 

[∵ Sum of ‘n’ consecutive odd number = n² ] 

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9² = 9 x 9 = 81 

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = 13² = 13 x 13 = 169