Addition of Odd Consecutive Numbers

Did you ever notice that by playing with numbers we can generated some cool patterns. One such pattern is generation of a square number by adding any number of consecutive odd integers, starting with one. Below is the pattern..

1 + 3 = 4 = 2²
1 + 3 + 5 = 9 = 3²
1 + 3 + 5 + 7 = 16 = 4²
1 + 3 + 5 + 7 + 9 = 25 = 5²
1 + 3 + 5 + 7 + 9 + 11 = 36 = 6²
1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7²
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8²
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81 = 9²
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 = 10²
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In general 1 + 3 + 5 + ........ + (2n-1)= n², where n is a positive integer.

Is it not cool! if you have any such patterns that you can generate by playing with numbers, then do share.