Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Find the radius of convergence, R, of the series. 00 n = 3 +7 +6 6n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

Find the radius of convergence, R, of the series. 00 n = 3 +7 +6 6n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 28RE: A ball has a bounce-back ratio 35 . of the height of the previous bounce. Write a series...
See similar textbooks
icon
Related questions
Question
100%

sum n = 3 to infinity (X ^ (n+6))/(6*n!)

Find the radius of convergence, R, of the series. n = 3 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) lim n→ co 00 Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. Step 2 +7 +6 6n! an +1 an lim n→ ∞ = = Simplifying, we get lim n→ ∞0 lim n→ ∞0 = || lim n→∞⁰ 6(n + 1)! Step 3 Therefore, we now have the following. an+ 1 a +7+7 6(n + 1)! + 6 6n! +7+7 6 Ix lim = |x|. n+1 1 n→ ∞⁰ n + 1 X n! +7+6 n+1 n!
Transcribed Image Text:Find the radius of convergence, R, of the series. n = 3 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) lim n→ co 00 Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. Step 2 +7 +6 6n! an +1 an lim n→ ∞ = = Simplifying, we get lim n→ ∞0 lim n→ ∞0 = || lim n→∞⁰ 6(n + 1)! Step 3 Therefore, we now have the following. an+ 1 a +7+7 6(n + 1)! + 6 6n! +7+7 6 Ix lim = |x|. n+1 1 n→ ∞⁰ n + 1 X n! +7+6 n+1 n!
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer