- #1
alnix
- 3
- 0
Homework Statement
serie ((-1)^(n-1)(x-2)^(n-1))/(5^n)
Homework Equations
how to find the interval of convergence for this?
How to Find the Interval of Convergence for this Series?
- Thread starter alnix
- Start date
-
- Tags
- Convergence Interval
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Homework Help Overview
The discussion revolves around finding the interval of convergence for the series given by the expression \((-1)^{n-1}(x-2)^{n-1}/(5^n)\). Participants are exploring methods to analyze the convergence of this series.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants suggest simplifying the series to a more recognizable form. There is a mention of using the ratio test to determine the radius of convergence, with a focus on calculating the limit of the ratio of consecutive terms.
Discussion Status
The discussion includes attempts to clarify the series expression and explore methods for determining convergence. Some participants provide guidance on using the ratio test, while others emphasize the importance of showing prior attempts in future threads.
Contextual Notes
There is a reminder for participants to demonstrate their efforts when posting problems, indicating a focus on learning and engagement in the homework help context.
serie ((-1)^(n-1)(x-2)^(n-1))/(5^n)
how to find the interval of convergence for this?
- #2
tiny-tim
Science Advisor
Homework Helper
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hi alnix! 
(try using the X2 button just above the Reply box
)
first, simplify it to something you can recognise!
(try using the X2 button just above the Reply box
)first, simplify it to something you can recognise!
- #3
lendav_rott
- 232
- 10
Before we can go anywhere, is this what you mean?
[tex]\frac{(-1)^{n-1}(x-2)^{n-1}}{5^n}[/tex]
[tex]\frac{(-1)^{n-1}(x-2)^{n-1}}{5^n}[/tex]
- #4
HallsofIvy
Science Advisor
Homework Helper
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The simplest way to determine the radius of convergence is to use the "ratio test".
[tex]a_n= \frac{(-1)^{n-1}(x- 2)^{n-1}}{5^n}[/tex]
[tex]a_{n+1}= \frac{(-1)^n(x- 2)^n}{5^{n+1}}[/tex]
What is [itex]\left|\frac{a_{n+1}}{a_n}\right|[/itex]? What is the limit of that as n goes to infinity? For what x is that limit less than 1?
[tex]a_n= \frac{(-1)^{n-1}(x- 2)^{n-1}}{5^n}[/tex]
[tex]a_{n+1}= \frac{(-1)^n(x- 2)^n}{5^{n+1}}[/tex]
What is [itex]\left|\frac{a_{n+1}}{a_n}\right|[/itex]? What is the limit of that as n goes to infinity? For what x is that limit less than 1?
- #5
Mark44
Mentor
- 38,110
- 10,673
To all who have responded in this thread - if someone posts a problem with no effort shown, please use the Report button to let the mentors know.
Alnix, I am closing this thread. Please start a new thread and be sure to show what you have attempted.
Alnix, I am closing this thread. Please start a new thread and be sure to show what you have attempted.
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