Sum of the first 1355 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 1355 square numbers, you ask? Here we will give you the formula to calculate the first 1355 square numbers and then we will show you how to calculate the first 1355 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 1355 square numbers, we enter n = 1355 into our formula to get this:

		1355(1355 + 1) × (2(1355) + 1)
		6

First, calculate each section of the numerator: 1355(1355 + 1) equals 1837380 and (2(1355) + 1) equals 2711. Therefore, the problem above becomes this:

		1837380 × 2711
		6

Next, we calculate 1837380 times 2711 which equals 4981137180. Now our problem looks like this:

		4981137180
		6

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

4981137180 ÷ 6 = 830189530

There you go. The sum of the first 1355 square numbers is 830189530.

You may also be interested to know that if you list the first 1355 square numbers 1, 2, 9, etc., the 1355th square number is 1836025.

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