Question

What is the sum of the infinite geometric series? 120 + 20+ 10/3 + 5/9+...

Answer 1

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

$\frac{a_{1} }{1 - r}$ = $\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =$ $\frac{120 \times 6}{5}$ = 144.

Step-by-step explanation:

i) from the given series we can see that the first term is $a_{1 }$ = 120.

ii) let the common ratio be r.

iii) the second term is 20 = 120 × r

   therefore r = 20 ÷ 120 = $\dfrac{1}{6}$

iv) the third term is $\frac{10}{3}$ = 20 × r

    therefore r = $\dfrac{10}{3}$ ÷ 20 = $\dfrac{1}{6}$

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

$\frac{a_{1} }{1 - r}$ = $\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =$ $\frac{120 \times 6}{5}$ = 144.