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 1 + 3 + 5 + 7 + 9 = 5² = 25.

Your turn

Three to try in your head — tap what you get.

1 + 3 + 5 + ... + 17

1 + 3 + 5 + ... + 19

1 + 3 + 5 + ... + 11

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