When a set of natural numbers is under consideration, if we add first consecutive 'n' odd natural numbers(i.e. from 1 ) we get a complete square whose root is 'n' itself.
e.g. first 5 consecutive odd natural numbers are, 1,3,5,7,9 so, 1+3+5+7+9 = 25. We get √25 = 5 . or e.g. first 6 consecutive odd natural numbers are, 1,3,5,7,9,11 so, 1+3+5+7+9+11 = 36 We get √36 = 6 .
I observed this while working on an algorithm to identify perfect squares. Has this been observed by any mathematician before?