Sum of the first 1307 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 1307 square numbers, you ask? Here we will give you the formula to calculate the first 1307 square numbers and then we will show you how to calculate the first 1307 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 1307 square numbers, we enter n = 1307 into our formula to get this:

		1307(1307 + 1) × (2(1307) + 1)
		6

First, calculate each section of the numerator: 1307(1307 + 1) equals 1709556 and (2(1307) + 1) equals 2615. Therefore, the problem above becomes this:

		1709556 × 2615
		6

Next, we calculate 1709556 times 2615 which equals 4470488940. Now our problem looks like this:

		4470488940
		6

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

4470488940 ÷ 6 = 745081490

There you go. The sum of the first 1307 square numbers is 745081490.

You may also be interested to know that if you list the first 1307 square numbers 1, 2, 9, etc., the 1307th square number is 1708249.

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