Got the idea from this tweet.
We can represent the sum of the first n
odd numbers as a tree where each row has a number of items equal to the corresponding odd number:
- the 1st row has as many items as the 1st odd number,
1 = 2·1 - 1
,1
item in the middle - the 2nd row has as many items as the 2nd odd number,
3 = 2·2 - 1
,1
item in the middle and1 = 2 - 1
item on each of the two lateral sides (branches) - the 3rd row has as many items as the 3rd odd number,
5 = 2·3 - 1
,1
item in the middle and2 = 3 - 1
items on each of the two lateral sides (branches)