Sum of the first 1658 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 1658 square numbers, you ask? Here we will give you the formula to calculate the first 1658 square numbers and then we will show you how to calculate the first 1658 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 1658 square numbers, we enter n = 1658 into our formula to get this:

		1658(1658 + 1) × (2(1658) + 1)
		6

First, calculate each section of the numerator: 1658(1658 + 1) equals 2750622 and (2(1658) + 1) equals 3317. Therefore, the problem above becomes this:

		2750622 × 3317
		6

Next, we calculate 2750622 times 3317 which equals 9123813174. Now our problem looks like this:

		9123813174
		6

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

9123813174 ÷ 6 = 1520635529

There you go. The sum of the first 1658 square numbers is 1520635529.

You may also be interested to know that if you list the first 1658 square numbers 1, 2, 9, etc., the 1658th square number is 2748964.

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