Sum of the first 742 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 742 square numbers, you ask? Here we will give you the formula to calculate the first 742 square numbers and then we will show you how to calculate the first 742 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 742 square numbers, we enter n = 742 into our formula to get this:

		742(742 + 1) × (2(742) + 1)
		6

First, calculate each section of the numerator: 742(742 + 1) equals 551306 and (2(742) + 1) equals 1485. Therefore, the problem above becomes this:

		551306 × 1485
		6

Next, we calculate 551306 times 1485 which equals 818689410. Now our problem looks like this:

		818689410
		6

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

818689410 ÷ 6 = 136448235

There you go. The sum of the first 742 square numbers is 136448235.

You may also be interested to know that if you list the first 742 square numbers 1, 2, 9, etc., the 742nd square number is 550564.

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