Sum of the first 43 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 43 square numbers, you ask? Here we will give you the formula to calculate the first 43 square numbers and then we will show you how to calculate the first 43 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 43 square numbers, we enter n = 43 into our formula to get this:

		43(43 + 1) × (2(43) + 1)
		6

First, calculate each section of the numerator: 43(43 + 1) equals 1892 and (2(43) + 1) equals 87. Therefore, the problem above becomes this:

		1892 × 87
		6

Next, we calculate 1892 times 87 which equals 164604. Now our problem looks like this:

		164604
		6

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

164604 ÷ 6 = 27434

There you go. The sum of the first 43 square numbers is 27434.

You may also be interested to know that if you list the first 43 square numbers 1, 2, 9, etc., the 43rd square number is 1849.

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