Without adding, find the sum

• 1 + 3 + 5 + 7 + 9

• 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

• 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Answer

• Here, there are five odd numbers. Therefore square of 5 is 25. 1 + 3 + 5 + 7 + 9 = 5² = 25

• Here, there are ten odd numbers. Therefore square of 10 is 100. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10² = 100

• Here, there are twelve odd numbers. Therefore square of 12 is 144.

1 + 3 +5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = 12² = 144