Finding Radius of Interval Convergence: \sum x^n/2^n

[Lance WIlliam]

Homework Statement

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

I really don't have a clue on which way I should go.
Just a hint would be great:)

Homework Equations

The Attempt at a Solution

 

[Dick]

Hint: ratio test.

 

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