Sum of the first 774 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 774 square numbers, you ask? Here we will give you the formula to calculate the first 774 square numbers and then we will show you how to calculate the first 774 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 774 square numbers, we enter n = 774 into our formula to get this:

		774(774 + 1) × (2(774) + 1)
		6

First, calculate each section of the numerator: 774(774 + 1) equals 599850 and (2(774) + 1) equals 1549. Therefore, the problem above becomes this:

		599850 × 1549
		6

Next, we calculate 599850 times 1549 which equals 929167650. Now our problem looks like this:

		929167650
		6

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

929167650 ÷ 6 = 154861275

There you go. The sum of the first 774 square numbers is 154861275.

You may also be interested to know that if you list the first 774 square numbers 1, 2, 9, etc., the 774th square number is 599076.

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