# Homework Help: Radius and interval

1. Jul 27, 2008

### Lance WIlliam

1. The problem statement, all variables and given/known data

Finding the Radius of interval convergence of $$\sum$$ n=1(theres a infinity on the sigma), "x^n/2^n"

I really dont have a clue on which way I should go.
Just a hint would be great:)

2. Relevant equations

3. The attempt at a solution

2. Jul 27, 2008

### Dick

Hint: ratio test.

3. Jul 27, 2008

### HallsofIvy

You almost always use the ratio test to find the radius of convergence of a power series. For this particular problem you may find that the root test is simpler. But for most power series the ratio test is simplest.

Ratio test: The series $\sum a_n$ converges absolutely if
[tex]\lim_{n\rightarrow \infty}\frac{a_{n+1}}{a_n}< 1[/itex]
It diverges if that limit is larger than one and may converge absolutely, converge conditionally, or diverge if the limit is equal to 1.

Root test: The series $\sum a_n$ converges absolutely if
[tex]\lim_{n\rightarrow \infty}\left( ^n\sqrt{a_n}\right)< 1[/itex]
It diverges if that limit is larger than one and may converge absolutely, converge conditionally, or diverge if the limit is equal to 1.

Last edited by a moderator: Jul 27, 2008