a)
[tex]\it S_n=\dfrac{1}{3}\cdot\dfrac{\dfrac{1}{3^{n-1}}-1}{\dfrac{1}{3}-1}=\dfrac{1}{3}\cdot\dfrac{\dfrac{3^{n-1}-1}{3^{n-1}}}{\dfrac{2}{3}}= \dfrac{1}{2}\cdot\dfrac{3^{n-1}-1}{3^{n-1}}=\dfrac{1}{2}-\dfrac{1}{2\cdot3^{n-1}}[/tex]
b)
[tex]\it S_n=\dfrac{1}{3}+\dfrac{3^{n-1}-1}{3-1}=\dfrac{1}{3}+\dfrac{3^{n-1}-1}{2}=\dfrac{3^{n}-1}{6}[/tex]
