Sum of the first 1616 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 1616 square numbers, you ask? Here we will give you the formula to calculate the first 1616 square numbers and then we will show you how to calculate the first 1616 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 1616 square numbers, we enter n = 1616 into our formula to get this:

		1616(1616 + 1) × (2(1616) + 1)
		6

First, calculate each section of the numerator: 1616(1616 + 1) equals 2613072 and (2(1616) + 1) equals 3233. Therefore, the problem above becomes this:

		2613072 × 3233
		6

Next, we calculate 2613072 times 3233 which equals 8448061776. Now our problem looks like this:

		8448061776
		6

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

8448061776 ÷ 6 = 1408010296

There you go. The sum of the first 1616 square numbers is 1408010296.

You may also be interested to know that if you list the first 1616 square numbers 1, 2, 9, etc., the 1616th square number is 2611456.

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