Sum of the first 253 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 253 square numbers, you ask? Here we will give you the formula to calculate the first 253 square numbers and then we will show you how to calculate the first 253 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 253 square numbers, we enter n = 253 into our formula to get this:

		253(253 + 1) × (2(253) + 1)
		6

First, calculate each section of the numerator: 253(253 + 1) equals 64262 and (2(253) + 1) equals 507. Therefore, the problem above becomes this:

		64262 × 507
		6

Next, we calculate 64262 times 507 which equals 32580834. Now our problem looks like this:

		32580834
		6

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

32580834 ÷ 6 = 5430139

There you go. The sum of the first 253 square numbers is 5430139.

You may also be interested to know that if you list the first 253 square numbers 1, 2, 9, etc., the 253rd square number is 64009.

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