Sum of the first 734 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 734 square numbers, you ask? Here we will give you the formula to calculate the first 734 square numbers and then we will show you how to calculate the first 734 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 734 square numbers, we enter n = 734 into our formula to get this:

		734(734 + 1) × (2(734) + 1)
		6

First, calculate each section of the numerator: 734(734 + 1) equals 539490 and (2(734) + 1) equals 1469. Therefore, the problem above becomes this:

		539490 × 1469
		6

Next, we calculate 539490 times 1469 which equals 792510810. Now our problem looks like this:

		792510810
		6

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

792510810 ÷ 6 = 132085135

There you go. The sum of the first 734 square numbers is 132085135.

You may also be interested to know that if you list the first 734 square numbers 1, 2, 9, etc., the 734th square number is 538756.

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