Solve for S
\left\{\begin{matrix}S=-\frac{U\left(1-q\right)q^{n}}{q^{n}-1}\text{, }&\left(q=0\text{ and }n>0\right)\text{ or }\left(n\neq 0\text{ and }q\neq -1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }q<0\right)\text{ or }\left(q<0\text{ and }Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(n\neq 0\text{ and }q\neq 1\text{ and }q>0\right)\\S\in \mathrm{R}\text{, }&q=-1\text{ and }Numerator(n)\text{bmod}2=0\text{ and }U=0\text{ and }Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\end{matrix}\right.
Solve for U
\left\{\begin{matrix}U\in \mathrm{R}\text{, }&S=0\text{ and }q=0\text{ and }n>0\\U=-\frac{S\left(q^{n}-1\right)}{\left(1-q\right)q^{n}}\text{, }&n\neq 0\text{ and }q\neq 1\text{ and }\left(Denominator(n)\text{bmod}2=1\text{ or }q\neq -1\right)\text{ and }\left(Numerator(n)\text{bmod}2=1\text{ or }q\neq -1\right)\text{ and }\left(q>0\text{ or }Denominator(n)\text{bmod}2=1\right)\text{ and }q\neq 0\end{matrix}\right.
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