Sum of the first 1375 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 1375 square numbers, you ask? Here we will give you the formula to calculate the first 1375 square numbers and then we will show you how to calculate the first 1375 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 1375 square numbers, we enter n = 1375 into our formula to get this:

		1375(1375 + 1) × (2(1375) + 1)
		6

First, calculate each section of the numerator: 1375(1375 + 1) equals 1892000 and (2(1375) + 1) equals 2751. Therefore, the problem above becomes this:

		1892000 × 2751
		6

Next, we calculate 1892000 times 2751 which equals 5204892000. Now our problem looks like this:

		5204892000
		6

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

5204892000 ÷ 6 = 867482000

There you go. The sum of the first 1375 square numbers is 867482000.

You may also be interested to know that if you list the first 1375 square numbers 1, 2, 9, etc., the 1375th square number is 1890625.

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