Sum of the first 1246 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 1246 square numbers, you ask? Here we will give you the formula to calculate the first 1246 square numbers and then we will show you how to calculate the first 1246 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 1246 square numbers, we enter n = 1246 into our formula to get this:

		1246(1246 + 1) × (2(1246) + 1)
		6

First, calculate each section of the numerator: 1246(1246 + 1) equals 1553762 and (2(1246) + 1) equals 2493. Therefore, the problem above becomes this:

		1553762 × 2493
		6

Next, we calculate 1553762 times 2493 which equals 3873528666. Now our problem looks like this:

		3873528666
		6

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

3873528666 ÷ 6 = 645588111

There you go. The sum of the first 1246 square numbers is 645588111.

You may also be interested to know that if you list the first 1246 square numbers 1, 2, 9, etc., the 1246th square number is 1552516.

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