Square number is sum of consecutive odd numbers

Last updated at April 16, 2024 by

Let’s add consecutive odd numbers 

Number of Odd Number

Sum of Consecutive Odd Numbers

1

1

= 1 = 1 2

2

1 + 3

= 4 = 2 2

3

1 + 3 + 5

= 9 = 3 2

4

1 + 3 + 5 + 7

= 16 = 4 2

5

1 + 3 + 5 + 7 + 9

= 25 = 5 2

6

1 + 3 + 5 + 7 + 9 + 11

= 36 = 6 2

7

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

= 49 = 7 2

∴ Sum of n Odd Number = n 2

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo