Sum of the first 3958 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 3958 square numbers, you ask? Here we will give you the formula to calculate the first 3958 square numbers and then we will show you how to calculate the first 3958 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 3958 square numbers, we enter n = 3958 into our formula to get this:

		3958(3958 + 1) × (2(3958) + 1)
		6

First, calculate each section of the numerator: 3958(3958 + 1) equals 15669722 and (2(3958) + 1) equals 7917. Therefore, the problem above becomes this:

		15669722 × 7917
		6

Next, we calculate 15669722 times 7917 which equals 124057189074. Now our problem looks like this:

		124057189074
		6

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

124057189074 ÷ 6 = 20676198179

There you go. The sum of the first 3958 square numbers is 20676198179.

You may also be interested to know that if you list the first 3958 square numbers 1, 2, 9, etc., the 3958th square number is 15665764.

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