What is the sum of all the odd numbers from 1 to 961?

Sum of all the odd numbers from 1 to 961

To calculate the sum of all the odd numbers from 1 to 961, we simply add up all the odd numbers from 1 up to 961.

When we add up 1 + 3 + 5 ... all the way to 961, we get the following answer:

231361

What we find interesting is that when you add up all the odd numbers from 1 to any number, the sum will always be a perfect square.

The sum of odd numbers from 1 to 961 is no exception. To prove that the result is a perfect square, the square root of the result above should be an integer (whole number), which it is:

√231361 = 481

To summarize, the sum of all the odd numbers from 1 to 961 is 231361 and the sum is a perfect square.

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Sum of all the odd numbers from 1 to 962
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