Sum of the first 763 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 763 square numbers, you ask? Here we will give you the formula to calculate the first 763 square numbers and then we will show you how to calculate the first 763 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 763 square numbers, we enter n = 763 into our formula to get this:

		763(763 + 1) × (2(763) + 1)
		6

First, calculate each section of the numerator: 763(763 + 1) equals 582932 and (2(763) + 1) equals 1527. Therefore, the problem above becomes this:

		582932 × 1527
		6

Next, we calculate 582932 times 1527 which equals 890137164. Now our problem looks like this:

		890137164
		6

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

890137164 ÷ 6 = 148356194

There you go. The sum of the first 763 square numbers is 148356194.

You may also be interested to know that if you list the first 763 square numbers 1, 2, 9, etc., the 763rd square number is 582169.

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