Sum of the first 775 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 775 square numbers, you ask? Here we will give you the formula to calculate the first 775 square numbers and then we will show you how to calculate the first 775 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 775 square numbers, we enter n = 775 into our formula to get this:

		775(775 + 1) × (2(775) + 1)
		6

First, calculate each section of the numerator: 775(775 + 1) equals 601400 and (2(775) + 1) equals 1551. Therefore, the problem above becomes this:

		601400 × 1551
		6

Next, we calculate 601400 times 1551 which equals 932771400. Now our problem looks like this:

		932771400
		6

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

932771400 ÷ 6 = 155461900

There you go. The sum of the first 775 square numbers is 155461900.

You may also be interested to know that if you list the first 775 square numbers 1, 2, 9, etc., the 775th square number is 600625.

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