Sum of the first 1370 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 1370 square numbers, you ask? Here we will give you the formula to calculate the first 1370 square numbers and then we will show you how to calculate the first 1370 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 1370 square numbers, we enter n = 1370 into our formula to get this:

		1370(1370 + 1) × (2(1370) + 1)
		6

First, calculate each section of the numerator: 1370(1370 + 1) equals 1878270 and (2(1370) + 1) equals 2741. Therefore, the problem above becomes this:

		1878270 × 2741
		6

Next, we calculate 1878270 times 2741 which equals 5148338070. Now our problem looks like this:

		5148338070
		6

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

5148338070 ÷ 6 = 858056345

There you go. The sum of the first 1370 square numbers is 858056345.

You may also be interested to know that if you list the first 1370 square numbers 1, 2, 9, etc., the 1370th square number is 1876900.

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