\(S=1+3+3^2+3^3+-+3^{99}\)
\(\Rightarrow3S=3\left(1+3+3^2+3^3+-.+3^{99}\right)\)
\(\Rightarrow3S=3+3^2+3^3+3^4+-.+3^{100}\)
\(\Rightarrow3S-S=\left(3+3^2+3^3+3^4+-.+3^{100}\right)-\left(1+3+3^2+3^3+-.+3^{99}\right)\)\(\Rightarrow2S=3^{100}-1\Rightarrow S=\dfrac{3^{100}-1}{2}\)