Sum of the first 745 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 745 square numbers, you ask? Here we will give you the formula to calculate the first 745 square numbers and then we will show you how to calculate the first 745 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 745 square numbers, we enter n = 745 into our formula to get this:

		745(745 + 1) × (2(745) + 1)
		6

First, calculate each section of the numerator: 745(745 + 1) equals 555770 and (2(745) + 1) equals 1491. Therefore, the problem above becomes this:

		555770 × 1491
		6

Next, we calculate 555770 times 1491 which equals 828653070. Now our problem looks like this:

		828653070
		6

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

828653070 ÷ 6 = 138108845

There you go. The sum of the first 745 square numbers is 138108845.

You may also be interested to know that if you list the first 745 square numbers 1, 2, 9, etc., the 745th square number is 555025.

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