Sum of the first 757 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 757 square numbers, you ask? Here we will give you the formula to calculate the first 757 square numbers and then we will show you how to calculate the first 757 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 757 square numbers, we enter n = 757 into our formula to get this:

		757(757 + 1) × (2(757) + 1)
		6

First, calculate each section of the numerator: 757(757 + 1) equals 573806 and (2(757) + 1) equals 1515. Therefore, the problem above becomes this:

		573806 × 1515
		6

Next, we calculate 573806 times 1515 which equals 869316090. Now our problem looks like this:

		869316090
		6

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

869316090 ÷ 6 = 144886015

There you go. The sum of the first 757 square numbers is 144886015.

You may also be interested to know that if you list the first 757 square numbers 1, 2, 9, etc., the 757th square number is 573049.

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