\(S=1+3+3^2+...+3^{50}\)

\(\Rightarrow3S=3+3^2+3^3+...+3^{50}+3^{51}\)

\(\Rightarrow3S-S=2S=\left(3+3^2+3^3+...+3^{50}+3^{51}\right)-\left(1+3+3^2+...+3^{50}\right)=3^{51}-1\)

So \(S=\dfrac{3^{51}-1}{2}\)

Ta post S

S = 1+3(1+3^2+...+3^49)=1+3(S-3^50)

=>S=1+3S-3^51

=>2S=3^51-1=>S=\(\dfrac{3^{51-1}}{2}\)

=1+3+3^2+...+3^50

⇒3S=3+3^2+3^3+...+3^50+3^51

⇒3S−S=2S=(3+3^2+3^3+...+3^50+3^51)−(1+3+3^2+...+3^50)=3^51−1

So S=\(\dfrac{3^{51}-1}{2}\)

\(S=1+3+3^2+...+3^{50}\)

\(\Rightarrow3S=3+3^2+3^3+...+3^{51}\)

\(\Rightarrow3S-S=2S=3^{51}-1\)

So \(S=\dfrac{3^{51}-1}{2}\)