Sum of the first 246 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 246 square numbers, you ask? Here we will give you the formula to calculate the first 246 square numbers and then we will show you how to calculate the first 246 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 246 square numbers, we enter n = 246 into our formula to get this:

		246(246 + 1) × (2(246) + 1)
		6

First, calculate each section of the numerator: 246(246 + 1) equals 60762 and (2(246) + 1) equals 493. Therefore, the problem above becomes this:

		60762 × 493
		6

Next, we calculate 60762 times 493 which equals 29955666. Now our problem looks like this:

		29955666
		6

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

29955666 ÷ 6 = 4992611

There you go. The sum of the first 246 square numbers is 4992611.

You may also be interested to know that if you list the first 246 square numbers 1, 2, 9, etc., the 246th square number is 60516.

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