Sum of Consecutive Odds
The first N odd numbers always sum to N².
1 + 3 + 5 + 7 + 9 = 25
A 4 by 4 square sits inside a 5 by 5, and the L-shaped rim around it holds 9.
Every odd number is one of those rims: 1, then 3, then 5, then 7, then 9.
Five rims complete a 5 by 5 square, so .
Your turn
Three to try in your head — tap what you get.
1 + 3 + 5 + ... + 17
1 + 3 + 5 + ... + 19
1 + 3 + 5 + ... + 11
All 36 shortcuts: the Magic Tricks library.