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 }