Q4 of 239 Page 29

Express the following as a sum of consecutive odd numbers starting with 1
7²

We know that any square can be expressed as the sum of consecutive odd numbers starting from 1.

n² = 1 + 3 + 5 + … + (2n-1)

Therefore, 7² = 1 + 3 + 5 + … + (2 × 7-1)

= 1 + 3 + 5 + … + 13

= 1 + 3 + 5 + 7 + 9 + 11 + 13

Find the sum of the following numbers without actually adding the numbers.

1 + 3 + 5 + 7

Find the sum of the following numbers without actually adding the numbers.

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

Express the following as a sum of consecutive odd numbers starting with 1

9²

Express the following as a sum of consecutive odd numbers starting with 1

5²

Questions · 239

1. Real Number System

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 5 5 6 6 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 6 6 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 10 10 10 10 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 6 7 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 1 2 3

Express the following as a sum of consecutive odd numbers starting with 172