Sum of the first 741 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 741 square numbers, you ask? Here we will give you the formula to calculate the first 741 square numbers and then we will show you how to calculate the first 741 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 741 square numbers, we enter n = 741 into our formula to get this:

		741(741 + 1) × (2(741) + 1)
		6

First, calculate each section of the numerator: 741(741 + 1) equals 549822 and (2(741) + 1) equals 1483. Therefore, the problem above becomes this:

		549822 × 1483
		6

Next, we calculate 549822 times 1483 which equals 815386026. Now our problem looks like this:

		815386026
		6

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

815386026 ÷ 6 = 135897671

There you go. The sum of the first 741 square numbers is 135897671.

You may also be interested to know that if you list the first 741 square numbers 1, 2, 9, etc., the 741st square number is 549081.

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