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I need help with this practice problem solving It asks, does the series converge or diverge? At the bottom of the pic is question #2, choose one answer from the list provided

I need help with this practice problem solving It asks, does the series converge or-example-1
User Annelle
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7.2k points

1 Answer

6 votes

Given:


(1)/(4)+(1)/(3)+(4)/(9)+(16)/(27)+(64)/(81)+.......

Required:

To find whether the given series is convergent or divergent.

Step-by-step explanation:

The given series is geometric series.

And the common ratio r is,


\begin{gathered} r=((1)/(3))/((1)/(4)) \\ \\ =(4)/(3) \end{gathered}

As


|r|\ge1

that means the terms do not tend towards 0, as


n\rightarrow\infty

Therefore, the series is divergent.

Final Answer:

The given series is divergent, because the series is geometric and the absolute value of the common ratio is greater than 1.

User Efritz
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7.5k points
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