Solve s_{n}=3*[1-(-2)^n]/1+2

$$s _ { n } = \frac { 3 \times [ 1 - ( - 2 ) ^ { n } ] } { 1 + 2 }$$

Solve for n (complex solution)

$$n=\frac{\ln(1-s_{n})}{\ln(2)+\pi i}+\frac{2i\pi n_{1}}{\ln(2)+\pi i}$$

$$n_{1}\in \mathrm{Z}$$

$$s_{n}\neq 1$$

Solve for s_n (complex solution)

$$s_{n}=1-\left(-2\right)^{n}$$

Solve for n

$$n=\log_{2}\left(1-s_{n}\right)$$

$$s_{n}<1\text{ and }Numerator(\log_{2}\left(1-s_{n}\right))\text{bmod}2=0\text{ and }Denominator(\log_{2}\left(1-s_{n}\right))\text{bmod}2=1$$

Solve for s_n

$$s_{n}=1-\left(-2\right)^{n}$$

$$Denominator(n)\text{bmod}2=1$$