Sum of the first 62 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 62 square numbers, you ask? Here we will give you the formula to calculate the first 62 square numbers and then we will show you how to calculate the first 62 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 62 square numbers, we enter n = 62 into our formula to get this:

		62(62 + 1) × (2(62) + 1)
		6

First, calculate each section of the numerator: 62(62 + 1) equals 3906 and (2(62) + 1) equals 125. Therefore, the problem above becomes this:

		3906 × 125
		6

Next, we calculate 3906 times 125 which equals 488250. Now our problem looks like this:

		488250
		6

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

488250 ÷ 6 = 81375

There you go. The sum of the first 62 square numbers is 81375.

You may also be interested to know that if you list the first 62 square numbers 1, 2, 9, etc., the 62nd square number is 3844.

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