Consider the power series ∑n=1^∞((-6)^n)/(√(n)) (x+8)^n. Find the radius of convergence R. If it

Name: Consider the power series ∑n=1^∞((-6)^n)/(√(n)) (x+8)^n. Find the radius of convergence R. If it is infinite, type ïnfinityör ïnf.̈ Answer: R = (1)/(6) What is the interval of convergence? Answer (in interval notation): [-(49)/(6), -(47)/(6) ]
Uploaded: 2023-07-21T18:42:05-08:00
Duration: 3 min 28 s
Channel: Madhur L
Description: Consider the power series ∑n=1^∞((-6)^n)/(√(n)) (x+8)^n. Find the radius of convergence R. If it is infinite, type ïnfinityör ïnf.̈ Answer: R = (1)/(6) What is the interval of convergence? Answer (in interval notation): [-(49)/(6), -(47)/(6) ]

Step 1: To find the radius of convergence, we can use the ratio test. The ratio test states that

This problem has been solved

100% free to try

Question

Consider the power series \(\sum_{n=1}^{\infty} \frac{(-6)^n}{\sqrt{n}} (x+8)^n\). Find the radius of convergence R. If it is infinite, type \"infinity\" or \"inf\". Answer: R = \frac{1}{6} What is the interval of convergence? Answer (in interval notation): \( [-\frac{49}{6}, -\frac{47}{6} ] \)

          Consider the power series \(\sum_{n=1}^{\infty} \frac{(-6)^n}{\sqrt{n}} (x+8)^n\). Find the radius of convergence R. If it is infinite, type \"infinity\" or \"inf\". Answer: R = \frac{1}{6} What is the interval of convergence? Answer (in interval notation): \( [-\frac{49}{6}, -\frac{47}{6} ] \)

Consider the power series ∑n=1^∞((-6)^n)/(√(n)) (x+8)^n. Find the radius of convergence R. If it is infinite, type ïnfinityör ïnf.̈ Answer: R = (1)/(6) What is the interval of convergence? Answer (in interval notation): [-(49)/(6), -(47)/(6) ]

Added by Margaret B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/21/2023

Step 1

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a power series is less than 1, then the series converges. If the limit is greater than 1, then the series diverges. If the limit is exactly 1, the test is Show more…

Show all steps

Thanks for your feedback!

Consider the power series 6 x+8 n1 /n Find the radius of convergence R. If it is infinite, type "infinity or "inf" Answer: R What is the interval of convergence? Answer (in interval notation): 49 47 6