Sum of the first 1637 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 1637 square numbers, you ask? Here we will give you the formula to calculate the first 1637 square numbers and then we will show you how to calculate the first 1637 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 1637 square numbers, we enter n = 1637 into our formula to get this:

		1637(1637 + 1) × (2(1637) + 1)
		6

First, calculate each section of the numerator: 1637(1637 + 1) equals 2681406 and (2(1637) + 1) equals 3275. Therefore, the problem above becomes this:

		2681406 × 3275
		6

Next, we calculate 2681406 times 3275 which equals 8781604650. Now our problem looks like this:

		8781604650
		6

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

8781604650 ÷ 6 = 1463600775

There you go. The sum of the first 1637 square numbers is 1463600775.

You may also be interested to know that if you list the first 1637 square numbers 1, 2, 9, etc., the 1637th square number is 2679769.

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