Sum of the first 342 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 342 square numbers, you ask? Here we will give you the formula to calculate the first 342 square numbers and then we will show you how to calculate the first 342 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 342 square numbers, we enter n = 342 into our formula to get this:

		342(342 + 1) × (2(342) + 1)
		6

First, calculate each section of the numerator: 342(342 + 1) equals 117306 and (2(342) + 1) equals 685. Therefore, the problem above becomes this:

		117306 × 685
		6

Next, we calculate 117306 times 685 which equals 80354610. Now our problem looks like this:

		80354610
		6

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

80354610 ÷ 6 = 13392435

There you go. The sum of the first 342 square numbers is 13392435.

You may also be interested to know that if you list the first 342 square numbers 1, 2, 9, etc., the 342nd square number is 116964.

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