Answer: [tex]S_{n}[/tex] = a([tex]\frac{1-r^{n}} {1-r}[/tex]) when r[tex]\leq[/tex]1
and [tex]S_{n}[/tex] =[tex]a(\frac{r^{n}-1} {r-1})[/tex] when r[tex]\geq[/tex]1
Explanation:
where a is first term of geometric series
r = common ratio of geometric series
n= number of terms of geometric series
In the given series a=[tex]\frac{1}{2}[/tex]
r=[tex]\frac{2}{3}[/tex]
n=5
So, substituting the values in the equation for r[tex]\leq[/tex]1
you will get the required result
