- #1
kleyton
- 7
- 0
I have been working on representing the powers of numbers as a summation.
This is as far as I have gotten.
Power: 2
[itex]m^2 = \sum_{n=1}^m \left(2n -1\right)[/itex]
Power: 3
[itex]m^3 = \sum_{n=1}^m \left(3n^2 -3n +1\right)[/itex]
Power: 4
[itex]m^4 = \sum_{n=2}^m \left[6*(4n-6) * \left(\sum_{a=1}^{m-n+1} a\right)\right] + m^2[/itex]
I wanted to know if it is possible to simplify the equation for the 4th and 3rd power of a number so that the highest power in the equation in 1.
Thanks
This is as far as I have gotten.
Power: 2
[itex]m^2 = \sum_{n=1}^m \left(2n -1\right)[/itex]
Power: 3
[itex]m^3 = \sum_{n=1}^m \left(3n^2 -3n +1\right)[/itex]
Power: 4
[itex]m^4 = \sum_{n=2}^m \left[6*(4n-6) * \left(\sum_{a=1}^{m-n+1} a\right)\right] + m^2[/itex]
I wanted to know if it is possible to simplify the equation for the 4th and 3rd power of a number so that the highest power in the equation in 1.
Thanks