<s>[INST] Series $1^3-1.5^3+2^3-2.5^3+...$ I came across a question today...

Sum to $n$ term of the series $$1^3-1.5^3+2^3-2.5^3+...$$ is?

I divided this series in two different series $$\left(1^3+2^3+3^3+...\right)-\left(1.5^3+2.5^3+3.5^3+...\right)$$
$$\Rightarrow\sum^{\frac{n+1}{2}}_{r=1}r^3-\sum^{\frac{n-1}{2}}_{r=1}\left(r+\frac{1}{2}\right)^3$$
$$\Rightarrow\sum^{\frac{n+1}{2}}_{r=1}r^3-\sum^{\frac{n-1}{2}}_{r=1}\left(r^3+\frac{1}{8}+1.5r^2+0.75r\right)$$
I solved this and couldn't get to the answer. Am I doing it in the right way? 
 [/INST] Hints:  You can represent the series as $$(\frac{-n}2)^3$$
        Assume even number of terms 
        $$n^3 - (n+1)^3 = -(3n^2+3n+1)$$
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