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
[tex]S_n= \frac{a_1(1-r^n)}{1-r} [/tex]
[tex]S_n= \frac{( \frac{1}{3} )(1-(1/3)^4)}{1- \frac{1}{3}}[/tex]
[tex]S_n= \frac{( \frac{1}{3} )(1-(1/3)^4)}{\frac{2}{3}}[/tex]
multiply top and bottom by 3/2
[tex]S_n=( \frac{3}{6} )(1-(1/81))[/tex]
[tex]S_n=( \frac{1}{2} )( \frac{80}{81} )[/tex]
[tex]S_n= \frac{80}{162} [/tex]
[tex]S_n= \frac{40}{81} [/tex]
sum is 40/81
