Sum of the first 1255 square numbers

We define square numbers as numbers that when squared will equal a whole number. Thus, the list of the first square numbers starts with 1, 4, 9, 16, and so on.

What is the sum of the first 1255 square numbers, you ask? Here we will give you the formula to calculate the first 1255 square numbers and then we will show you how to calculate the first 1255 square numbers using the formula.

The formula to calculate the first n square numbers is displayed below:

		n(n + 1) × (2(n) + 1)
		6

To calculate the sum of the first 1255 square numbers, we enter n = 1255 into our formula to get this:

		1255(1255 + 1) × (2(1255) + 1)
		6

First, calculate each section of the numerator: 1255(1255 + 1) equals 1576280 and (2(1255) + 1) equals 2511. Therefore, the problem above becomes this:

		1576280 × 2511
		6

Next, we calculate 1576280 times 2511 which equals 3958039080. Now our problem looks like this:

		3958039080
		6

Finally, divide the numerator by the denominator to get our answer:

3958039080 ÷ 6 = 659673180

There you go. The sum of the first 1255 square numbers is 659673180.

You may also be interested to know that if you list the first 1255 square numbers 1, 2, 9, etc., the 1255th square number is 1575025.

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