These are partial sums for even and odd numbers already:
even:
S_n =\sum\limits_{k=0}^n {{2n^2(n+1)^2}}
odd:
S_n =\sum\limits_{k=0}^n {n^2(2n^2-1)}
and substracting even from odd partial sums gets me:
S_n =\sum\limits_{k=0}^n {-4^3-3n^2}
And that doesn't get me to:
S_n =...
Homework Statement
I have this series
1^{3}-2^{3}+3^{3}-4^{3}+5^{3}-6^{3} + \ldots
Homework Equations
and sequence of partial sums for this series that is:
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...