- #1
gbean
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Homework Statement
Find the radius of convergence of the power series:
a) [tex]\sum[/tex] z[tex]^{n!}[/tex]
n=0 to infinity
b) [tex]\sum[/tex] (n+2[tex]^{n}[/tex])z[tex]^{n}[/tex]
n=0 to infinity
Homework Equations
Radius = 1/(limsup n=>infinity |cn|^1/n)
The Attempt at a Solution
a) Is cn in this case just 1? And plugging it in, the radius is 1?
b) cn = n+2[tex]^{n}[/tex], so then limsup n=> infinity |n+2[tex]^{n}[/tex]|[tex]^{1/n}[/tex] => ?? I'm stuck at this point.
i'm also confused in general, is cn just a sequence of coefficients, and what is zn? And I have other formulas for figuring out the radius of convergence, such as the ratio test. I'm not sure when to use which methods. Thank you!