Sum of the first 1288 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 1288 square numbers, you ask? Here we will give you the formula to calculate the first 1288 square numbers and then we will show you how to calculate the first 1288 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 1288 square numbers, we enter n = 1288 into our formula to get this:

		1288(1288 + 1) × (2(1288) + 1)
		6

First, calculate each section of the numerator: 1288(1288 + 1) equals 1660232 and (2(1288) + 1) equals 2577. Therefore, the problem above becomes this:

		1660232 × 2577
		6

Next, we calculate 1660232 times 2577 which equals 4278417864. Now our problem looks like this:

		4278417864
		6

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

4278417864 ÷ 6 = 713069644

There you go. The sum of the first 1288 square numbers is 713069644.

You may also be interested to know that if you list the first 1288 square numbers 1, 2, 9, etc., the 1288th square number is 1658944.

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