Answer:
for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
Step-by-step explanation:
i) from the given series we can see that the first term is [tex]a_{1 }[/tex] = 120.
ii) let the common ratio be r.
iii) the second term is 20 = 120 × r
therefore r = 20 ÷ 120 = [tex]\dfrac{1}{6}[/tex]
iv) the third term is [tex]\frac{10}{3}[/tex] = 20 × r
therefore r = [tex]\dfrac{10}{3}[/tex] ÷ 20 = [tex]\dfrac{1}{6}[/tex]
v) for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
