The equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Geometric sequence are sequence that increase expoentially. The formula for calculating the sum of an exponential sequence is expressed as:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
where
From the given sequence
a= 1/3
r = 2/9 * 3 = 2/3
Substitute into the formula
[tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Hence the equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Learn more on geometric series here; https://brainly.com/question/24643676
