Find the radius of convergence, R, of the series. 00 x7 +9 9n! n = 2 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ +7 + 10 a, n+1 = lim 9(n + 1)! an n→ ∞o +7 +9 9n! = lim noo xn+10 9(n + 1)! Step 2 Simplifying, we get lim n→ ∞o X n! n! x7 +9

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
Question

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Find the radius of convergence, R, of the series.
00
x7 +9
9n!
n = 2
Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)
Step 1
We will use the Ratio Test to determine the radius of convergence.
We have the following.
lim
n→ ∞
+7 + 10
a,
n+1
=
lim
9(n + 1)!
an
n→ ∞o
+7 +9
9n!
=
lim
noo
xn+10
9(n + 1)!
Step 2
Simplifying, we get lim
n→ ∞o
X
n!
n!
x7 +9
Transcribed Image Text:Find the radius of convergence, R, of the series. 00 x7 +9 9n! n = 2 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. lim n→ ∞ +7 + 10 a, n+1 = lim 9(n + 1)! an n→ ∞o +7 +9 9n! = lim noo xn+10 9(n + 1)! Step 2 Simplifying, we get lim n→ ∞o X n! n! x7 +9
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