Sum of the first 29 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 29 square numbers, you ask? Here we will give you the formula to calculate the first 29 square numbers and then we will show you how to calculate the first 29 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 29 square numbers, we enter n = 29 into our formula to get this:

		29(29 + 1) × (2(29) + 1)
		6

First, calculate each section of the numerator: 29(29 + 1) equals 870 and (2(29) + 1) equals 59. Therefore, the problem above becomes this:

		870 × 59
		6

Next, we calculate 870 times 59 which equals 51330. Now our problem looks like this:

		51330
		6

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

51330 ÷ 6 = 8555

There you go. The sum of the first 29 square numbers is 8555.

You may also be interested to know that if you list the first 29 square numbers 1, 2, 9, etc., the 29th square number is 841.

Sum of Square Numbers Calculator
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