Question

Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.1/5 + 1/10 + 1/20 + 1/40 + ….Infinitearithmeticgeometricfinite

Answer 1

geometric

infinite

Step-by-step explanation:

Correct on Odyssey..

Answer 2

Given:

Given the series

`(1)/(5)+(1)/(10)+(1)/(20)+(1)/(40)+...`

Required: Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.

Step-by-step explanation:

The given series is a geometric series as the terms of the series are 1/2 times its previous term.

`\begin{gathered} a_2=(1)/(10)=(1)/(2)\cdot(1)/(5)=(1)/(2)a_1 \\ a_3=(1)/(20)=(1)/(2)\cdot(1)/(10)=(1)/(2)a_2 \\ a_4=(1)/(40)=(1)/(2)\cdot(1)/(20)=(1)/(2)a_3 \end{gathered}`

So, the given series is a geometric series with first term, a = 1/5 and common difference, d = 1/2.

The three dots at the end of the series means the series is continuing. So, it is an infinite series.

Final Answer: The given series is an infinite geometric series.