Sum of the first 1652 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 1652 square numbers, you ask? Here we will give you the formula to calculate the first 1652 square numbers and then we will show you how to calculate the first 1652 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 1652 square numbers, we enter n = 1652 into our formula to get this:

		1652(1652 + 1) × (2(1652) + 1)
		6

First, calculate each section of the numerator: 1652(1652 + 1) equals 2730756 and (2(1652) + 1) equals 3305. Therefore, the problem above becomes this:

		2730756 × 3305
		6

Next, we calculate 2730756 times 3305 which equals 9025148580. Now our problem looks like this:

		9025148580
		6

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

9025148580 ÷ 6 = 1504191430

There you go. The sum of the first 1652 square numbers is 1504191430.

You may also be interested to know that if you list the first 1652 square numbers 1, 2, 9, etc., the 1652nd square number is 2729104.

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