## Related questions with answers

Question

Use a geometric series or the nth-Term Test to determine the convergence or divergence of the series. $\sum_{n=0}^{\infty} 9^{-n}$

Solution

VerifiedAnswered 7 months ago

Answered 7 months ago

Step 1

1 of 2$\color{#4257b2}{\sum_{n=0}^{\infty} 9^{-n}}$

$\hspace*{5mm}$Now is

$\begin{align*} \lim _{n \rightarrow \infty} \frac{1}{9^{n}} &=\frac{1}{9^{\infty}} \\ &=0 \end{align*}$

$\hspace*{45mm}$$\text{\textcolor{#c34632}{The series converges.}}$

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