Discover the Formula and Methods for Calculating the Sum of Cubes in Mathematics

Sum of Cubes

The sum of cubes refers to the sum of a series of perfect cubes

The sum of cubes refers to the sum of a series of perfect cubes. A perfect cube is a number that can be expressed as the product of an integer and itself, raised to the power of 3.

The formula for the sum of cubes is:

S = 1^3 + 2^3 + 3^3 + … + n^3

Where S is the sum of the cubes and n is the number of terms in the series.

To find the sum of cubes, there are two methods you can use:

1. Using the formula for the sum of cubes:

The formula for the sum of cubes allows you to find the sum directly without having to calculate each term individually. It is:

S = (n * (n + 1) / 2)^2

For example, if you want to find the sum of cubes of the first 5 numbers, you can substitute n = 5 into the formula:

S = (5 * (5 + 1) / 2)^2 = (5 * 6 / 2)^2 = (30 / 2)^2 = 15^2 = 225

So the sum of cubes of the first 5 numbers is 225.

2. Summing the cubes individually:

If you want to find the sum of cubes for a smaller range of numbers or if you prefer to calculate each term individually, you can add the cubes of each number together.

For example, let’s find the sum of cubes for the first 4 numbers:

S = 1^3 + 2^3 + 3^3 + 4^3

S = 1 + 8 + 27 + 64

S = 100

So the sum of cubes of the first 4 numbers is 100.

In summary, the sum of cubes refers to the sum of a series of perfect cubes. You can find it using the formula (n * (n + 1) / 2)^2 or by adding the cubes of each number individually.

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