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Find the interval of convergence. Sum of (x/16)^n from n = 0 to infinity.

Question:

Find the interval of convergence.

{eq}\sum_{n=0}^{\infty} (\frac{x}{16})^n {/eq}

Find The Radius Of Convergence:

Use the Root Test to compute the convergence interval

If {eq}\lim _{n\to \infty }|a_n|^{\frac{1}{n}}=L{/eq} and

If {eq}L<1{/eq} then {eq}\sum a_n{/eq} converges

If {eq}L=1{/eq}, then the test is inconclusive

Answer and Explanation:

Consider the series

{eq}\sum _{n=0}^{\infty \:}\left(\frac{x}{16}\right)^n {/eq}

Apply the Root Test:

{eq}\lim _{n\to \infty \:}...

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Learn more about this topic:

Power Series: Formula & Examples

from Precalculus: Help and Review

Chapter 2 / Lesson 10
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