Sum of the first 1474 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 1474 square numbers, you ask? Here we will give you the formula to calculate the first 1474 square numbers and then we will show you how to calculate the first 1474 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 1474 square numbers, we enter n = 1474 into our formula to get this:

		1474(1474 + 1) × (2(1474) + 1)
		6

First, calculate each section of the numerator: 1474(1474 + 1) equals 2174150 and (2(1474) + 1) equals 2949. Therefore, the problem above becomes this:

		2174150 × 2949
		6

Next, we calculate 2174150 times 2949 which equals 6411568350. Now our problem looks like this:

		6411568350
		6

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

6411568350 ÷ 6 = 1068594725

There you go. The sum of the first 1474 square numbers is 1068594725.

You may also be interested to know that if you list the first 1474 square numbers 1, 2, 9, etc., the 1474th square number is 2172676.

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