Sum of the first 270 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 270 square numbers, you ask? Here we will give you the formula to calculate the first 270 square numbers and then we will show you how to calculate the first 270 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 270 square numbers, we enter n = 270 into our formula to get this:

		270(270 + 1) × (2(270) + 1)
		6

First, calculate each section of the numerator: 270(270 + 1) equals 73170 and (2(270) + 1) equals 541. Therefore, the problem above becomes this:

		73170 × 541
		6

Next, we calculate 73170 times 541 which equals 39584970. Now our problem looks like this:

		39584970
		6

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

39584970 ÷ 6 = 6597495

There you go. The sum of the first 270 square numbers is 6597495.

You may also be interested to know that if you list the first 270 square numbers 1, 2, 9, etc., the 270th square number is 72900.

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