Sum of the first 740 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 740 square numbers, you ask? Here we will give you the formula to calculate the first 740 square numbers and then we will show you how to calculate the first 740 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 740 square numbers, we enter n = 740 into our formula to get this:

		740(740 + 1) × (2(740) + 1)
		6

First, calculate each section of the numerator: 740(740 + 1) equals 548340 and (2(740) + 1) equals 1481. Therefore, the problem above becomes this:

		548340 × 1481
		6

Next, we calculate 548340 times 1481 which equals 812091540. Now our problem looks like this:

		812091540
		6

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

812091540 ÷ 6 = 135348590

There you go. The sum of the first 740 square numbers is 135348590.

You may also be interested to know that if you list the first 740 square numbers 1, 2, 9, etc., the 740th square number is 547600.

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