Question

sum to infinity to series 108,36,12,4,....​

Answer 1

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Answer 2

Sum of infinite terms of the series is 162.

Step-by-step explanation:

The given series is 108, 36 , 12, 4.........

Common ratio 'r' = $\frac{\text{Successive term}}{\text{Previous term}}=\frac{36}{108}=\frac{1}{3}$

There is a common ratio of $\frac{1}{3}$ in every successive term to the previous term.

Therefore, it's a geometric series.

Sum of infinite terms of this series = $\frac{a}{1-r}$

Where a = first term of the series

r = common ratio

Here r < 1

Therefore, sum of infinite series = $\frac{108}{1-\frac{1}{3}}$

= $\frac{108}{\frac{2}{3}}$

= $108\times \frac{3}{2}$

= 162

Therefore, sum of infinite terms will be 162.

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