\sum ( 2 \pi n ) = k
Solve for n
\left\{\begin{matrix}n=\frac{k}{2\pi Σ}\text{, }&Σ\neq 0\\n\in \mathrm{R}\text{, }&k=0\text{ and }Σ=0\end{matrix}\right.
Solve for k
k=2\pi nΣ
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2\pi Σn=k
The equation is in standard form.
\frac{2\pi Σn}{2\pi Σ}=\frac{k}{2\pi Σ}
Divide both sides by 2Σ\pi .
n=\frac{k}{2\pi Σ}
Dividing by 2Σ\pi undoes the multiplication by 2Σ\pi .
k=Σ\times 2\pi n
Swap sides so that all variable terms are on the left hand side.
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