Sum of the first 63 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 63 square numbers, you ask? Here we will give you the formula to calculate the first 63 square numbers and then we will show you how to calculate the first 63 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 63 square numbers, we enter n = 63 into our formula to get this:

		63(63 + 1) × (2(63) + 1)
		6

First, calculate each section of the numerator: 63(63 + 1) equals 4032 and (2(63) + 1) equals 127. Therefore, the problem above becomes this:

		4032 × 127
		6

Next, we calculate 4032 times 127 which equals 512064. Now our problem looks like this:

		512064
		6

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

512064 ÷ 6 = 85344

There you go. The sum of the first 63 square numbers is 85344.

You may also be interested to know that if you list the first 63 square numbers 1, 2, 9, etc., the 63rd square number is 3969.

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