Discussion
The sum of all odd numbers from 1 to 51 is
Answer: A
The sum is 676.
The odd numbers from 1 to 51 are 1, 3, 5, ..., 51. There are \(\frac{51 + 1}{2} = 26\) of them, and the sum of the first \(n\) odd numbers is \(n^{2}\):
\[ 1 + 3 + 5 + \cdots + 51 = 26^{2} = 676 \]
625 is \(25^{2}\), the sum up to 49, which leaves out 51. 576 is \(24^{2}\), and 696 does not come from the formula.
The formula works because adding consecutive odd numbers builds perfect squares: 1, 1 + 3 = 4, 1 + 3 + 5 = 9, and so on.
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