Sum of the first 1597 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 1597 square numbers, you ask? Here we will give you the formula to calculate the first 1597 square numbers and then we will show you how to calculate the first 1597 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 1597 square numbers, we enter n = 1597 into our formula to get this:

		1597(1597 + 1) × (2(1597) + 1)
		6

First, calculate each section of the numerator: 1597(1597 + 1) equals 2552006 and (2(1597) + 1) equals 3195. Therefore, the problem above becomes this:

		2552006 × 3195
		6

Next, we calculate 2552006 times 3195 which equals 8153659170. Now our problem looks like this:

		8153659170
		6

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

8153659170 ÷ 6 = 1358943195

There you go. The sum of the first 1597 square numbers is 1358943195.

You may also be interested to know that if you list the first 1597 square numbers 1, 2, 9, etc., the 1597th square number is 2550409.

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