Sum of Cubes Calculator
Calculate the sum of cubes between two numbers quickly and easily.
Result:
Calculation Steps:
Understanding Sum of Cubes
In mathematics, the sum of cubes of the first n natural numbers has a closed-form formula. For a range of numbers from n1 to n2, we calculate it by finding the difference between the sum of cubes up to n2 and the sum of cubes up to n1-1.
Formula:
The sum of cubes from n1 to n2 is given by: $$ \sum_{i=n_1}^{n_2} i^3 = \left( \frac{n_2(n_2+1)}{2} \right)^2 - \left( \frac{(n_1-1)n_1}{2} \right)^2 $$
Example:
To find the sum of cubes from 2 to 4:
- Calculate sum of cubes up to 4: (1³ + 2³ + 3³ + 4³) = (4*(4+1)/2)² = 100
- Calculate sum of cubes up to 1 (4-1): (1³) = (1*(1+1)/2)² = 1
- Subtract the second from the first: 100 - 1 = 99
This calculator simplifies this process, providing you with quick and accurate results for any range of numbers. Use it for educational purposes, mathematical explorations, or any time you need to calculate sums of cubes efficiently.