Sum of the first 1607 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 1607 square numbers, you ask? Here we will give you the formula to calculate the first 1607 square numbers and then we will show you how to calculate the first 1607 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 1607 square numbers, we enter n = 1607 into our formula to get this:

		1607(1607 + 1) × (2(1607) + 1)
		6

First, calculate each section of the numerator: 1607(1607 + 1) equals 2584056 and (2(1607) + 1) equals 3215. Therefore, the problem above becomes this:

		2584056 × 3215
		6

Next, we calculate 2584056 times 3215 which equals 8307740040. Now our problem looks like this:

		8307740040
		6

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

8307740040 ÷ 6 = 1384623340

There you go. The sum of the first 1607 square numbers is 1384623340.

You may also be interested to know that if you list the first 1607 square numbers 1, 2, 9, etc., the 1607th square number is 2582449.

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