Sum of the first 341 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 341 square numbers, you ask? Here we will give you the formula to calculate the first 341 square numbers and then we will show you how to calculate the first 341 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 341 square numbers, we enter n = 341 into our formula to get this:

		341(341 + 1) × (2(341) + 1)
		6

First, calculate each section of the numerator: 341(341 + 1) equals 116622 and (2(341) + 1) equals 683. Therefore, the problem above becomes this:

		116622 × 683
		6

Next, we calculate 116622 times 683 which equals 79652826. Now our problem looks like this:

		79652826
		6

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

79652826 ÷ 6 = 13275471

There you go. The sum of the first 341 square numbers is 13275471.

You may also be interested to know that if you list the first 341 square numbers 1, 2, 9, etc., the 341st square number is 116281.

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