Determine whether the series is convergent or divergent. 1 + 1 / 16 + 1 / 81 + 1 / 256 + 1 / 625...

Question:

Determine whether the series is convergent or divergent.

{eq}1+\frac{1}{16}+\frac{1}{81}+\frac{1}{256}+\frac{1}{625}+... {/eq}

{eq}p= {/eq}

p-Series Test:

The p-series test for infinite series states that a p-series is a series in the form {eq}\displaystyle \; \sum_{n=1}^{\infty} \frac{1}{n^p} = \frac{1}{1^p}+\frac{1}{2^p}+\frac{1}{3^p}+\frac{1}{4^p}+\frac{1}{5^p}+ \cdots \; {/eq}, and that such a series is convergent if and only if {eq}\displaystyle \; p > 1 \; {/eq}.

Answer and Explanation:

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We have a series in the form {eq}\displaystyle \; 1+\frac{1}{16}+\frac{1}{81}+\frac{1}{256}+\frac{1}{625}+ \cdots =...

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P-Series: Definition & Examples

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Chapter 29 / Lesson 5
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This lesson is designed to help you understand a specific type of series called a p-series. You will determine if a series is a p-series, and you will learn to decide if a p-series converges or diverges.


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