Sum of the first 1507 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 1507 square numbers, you ask? Here we will give you the formula to calculate the first 1507 square numbers and then we will show you how to calculate the first 1507 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 1507 square numbers, we enter n = 1507 into our formula to get this:

		1507(1507 + 1) × (2(1507) + 1)
		6

First, calculate each section of the numerator: 1507(1507 + 1) equals 2272556 and (2(1507) + 1) equals 3015. Therefore, the problem above becomes this:

		2272556 × 3015
		6

Next, we calculate 2272556 times 3015 which equals 6851756340. Now our problem looks like this:

		6851756340
		6

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

6851756340 ÷ 6 = 1141959390

There you go. The sum of the first 1507 square numbers is 1141959390.

You may also be interested to know that if you list the first 1507 square numbers 1, 2, 9, etc., the 1507th square number is 2271049.

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