Sum of the first 159 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 159 square numbers, you ask? Here we will give you the formula to calculate the first 159 square numbers and then we will show you how to calculate the first 159 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 159 square numbers, we enter n = 159 into our formula to get this:

		159(159 + 1) × (2(159) + 1)
		6

First, calculate each section of the numerator: 159(159 + 1) equals 25440 and (2(159) + 1) equals 319. Therefore, the problem above becomes this:

		25440 × 319
		6

Next, we calculate 25440 times 319 which equals 8115360. Now our problem looks like this:

		8115360
		6

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

8115360 ÷ 6 = 1352560

There you go. The sum of the first 159 square numbers is 1352560.

You may also be interested to know that if you list the first 159 square numbers 1, 2, 9, etc., the 159th square number is 25281.

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