Sum of the first 1376 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 1376 square numbers, you ask? Here we will give you the formula to calculate the first 1376 square numbers and then we will show you how to calculate the first 1376 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 1376 square numbers, we enter n = 1376 into our formula to get this:

		1376(1376 + 1) × (2(1376) + 1)
		6

First, calculate each section of the numerator: 1376(1376 + 1) equals 1894752 and (2(1376) + 1) equals 2753. Therefore, the problem above becomes this:

		1894752 × 2753
		6

Next, we calculate 1894752 times 2753 which equals 5216252256. Now our problem looks like this:

		5216252256
		6

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

5216252256 ÷ 6 = 869375376

There you go. The sum of the first 1376 square numbers is 869375376.

You may also be interested to know that if you list the first 1376 square numbers 1, 2, 9, etc., the 1376th square number is 1893376.

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