Sum of the first 1290 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 1290 square numbers, you ask? Here we will give you the formula to calculate the first 1290 square numbers and then we will show you how to calculate the first 1290 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 1290 square numbers, we enter n = 1290 into our formula to get this:

		1290(1290 + 1) × (2(1290) + 1)
		6

First, calculate each section of the numerator: 1290(1290 + 1) equals 1665390 and (2(1290) + 1) equals 2581. Therefore, the problem above becomes this:

		1665390 × 2581
		6

Next, we calculate 1665390 times 2581 which equals 4298371590. Now our problem looks like this:

		4298371590
		6

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

4298371590 ÷ 6 = 716395265

There you go. The sum of the first 1290 square numbers is 716395265.

You may also be interested to know that if you list the first 1290 square numbers 1, 2, 9, etc., the 1290th square number is 1664100.

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