Sum of the first 137 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 137 square numbers, you ask? Here we will give you the formula to calculate the first 137 square numbers and then we will show you how to calculate the first 137 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 137 square numbers, we enter n = 137 into our formula to get this:

		137(137 + 1) × (2(137) + 1)
		6

First, calculate each section of the numerator: 137(137 + 1) equals 18906 and (2(137) + 1) equals 275. Therefore, the problem above becomes this:

		18906 × 275
		6

Next, we calculate 18906 times 275 which equals 5199150. Now our problem looks like this:

		5199150
		6

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

5199150 ÷ 6 = 866525

There you go. The sum of the first 137 square numbers is 866525.

You may also be interested to know that if you list the first 137 square numbers 1, 2, 9, etc., the 137th square number is 18769.

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