For questions 1-3, find the radius of convergence and the interval of convergence for each power series. 1. [40] sum_{n=1}^{infty} frac{(-1)^n x^n}{n}
Added by Brooke H.
Close
Step 1
The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms of a series is less than 1, then the series converges. In this case, we have: $$\lim_{n\to\infty} \frac{|a_{n+1}|}{|a_n|} = \lim_{n\to\infty} Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 86 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
need help solving this power series question
Ben B.
In Problems $1-4$, find the radius of convergence and interval of convergence for the given power series. $$ \sum_{n=0}^{\infty} \frac{(100)^{n}}{n !}(x+7)^{n} $$
Series Solutions of Linear Differential Equations
Solutions about Ordinary Points
In Problems $1-4$, find the radius of convergence and interval of convergence for the given power series. $$ \sum_{k=0}^{\infty} k !(x-1)^{k} $$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD