Sum of the first 15 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 15 square numbers, you ask? Here we will give you the formula to calculate the first 15 square numbers and then we will show you how to calculate the first 15 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 15 square numbers, we enter n = 15 into our formula to get this:

		15(15 + 1) × (2(15) + 1)
		6

First, calculate each section of the numerator: 15(15 + 1) equals 240 and (2(15) + 1) equals 31. Therefore, the problem above becomes this:

		240 × 31
		6

Next, we calculate 240 times 31 which equals 7440. Now our problem looks like this:

		7440
		6

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

7440 ÷ 6 = 1240

There you go. The sum of the first 15 square numbers is 1240.

You may also be interested to know that if you list the first 15 square numbers 1, 2, 9, etc., the 15th square number is 225.

Sum of Square Numbers Calculator
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