we see that the first term is a1 or 1/3
the common ratio is 1/3
the number of terms (n) is 4
so
\(S_n= \frac{a_1(1-r^n)}{1-r}\)
\(S_n= \frac{( \frac{1}{3} )(1-(1/3)^4)}{1- \frac{1}{3}}\)
\(S_n= \frac{( \frac{1}{3} )(1-(1/3)^4)}{\frac{2}{3}}\)
multiply top and bottom by 3/2
\(S_n=( \frac{3}{6} )(1-(1/81))\)
\(S_n=( \frac{1}{2} )( \frac{80}{81} )\)
\(S_n= \frac{80}{162}\)
\(S_n= \frac{40}{81}\)
sum is 40/81
