Sum of the first 340 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 340 square numbers, you ask? Here we will give you the formula to calculate the first 340 square numbers and then we will show you how to calculate the first 340 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 340 square numbers, we enter n = 340 into our formula to get this:

		340(340 + 1) × (2(340) + 1)
		6

First, calculate each section of the numerator: 340(340 + 1) equals 115940 and (2(340) + 1) equals 681. Therefore, the problem above becomes this:

		115940 × 681
		6

Next, we calculate 115940 times 681 which equals 78955140. Now our problem looks like this:

		78955140
		6

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

78955140 ÷ 6 = 13159190

There you go. The sum of the first 340 square numbers is 13159190.

You may also be interested to know that if you list the first 340 square numbers 1, 2, 9, etc., the 340th square number is 115600.

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