- #1
Dobsn
- 2
- 0
Homework Statement
I have this series
[itex]1^{3}-2^{3}+3^{3}-4^{3}+5^{3}-6^{3} + \ldots[/itex]
Homework Equations
and sequence of partial sums for this series that is:
[itex]S_n = \sum_{k=0}^{n}(-1)^{k+1} k^3 = \dfrac{1 + (-1)^n(4n^3 + 6n^2-1)}8 =\begin{cases} \dfrac{2n^3+3n^2}4; & n \text{ is even}\\ \dfrac{1-3n^2-2n^3}4; & n \text{ is odd} \end{cases}[/itex]
What I need to are finding the steps to this partial sums formula
The Attempt at a Solution
I've tried by finding partial sums for even and odd cubes and then substracting them, but it gives wrong solution.
Odd: [itex]n^2(2n^2-1)[/itex]
Even: [itex]2n^2(n+1)^2[/itex]
Any tip appreaciated. :)