Sum of the first 739 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 739 square numbers, you ask? Here we will give you the formula to calculate the first 739 square numbers and then we will show you how to calculate the first 739 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 739 square numbers, we enter n = 739 into our formula to get this:

		739(739 + 1) × (2(739) + 1)
		6

First, calculate each section of the numerator: 739(739 + 1) equals 546860 and (2(739) + 1) equals 1479. Therefore, the problem above becomes this:

		546860 × 1479
		6

Next, we calculate 546860 times 1479 which equals 808805940. Now our problem looks like this:

		808805940
		6

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

808805940 ÷ 6 = 134800990

There you go. The sum of the first 739 square numbers is 134800990.

You may also be interested to know that if you list the first 739 square numbers 1, 2, 9, etc., the 739th square number is 546121.

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