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azatkgz
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Homework Statement
Find the radius and interval of convergence for the following power series.
[tex]\sum_{n = 2}^{\infty}\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}x^n[/tex]
The Attempt at a Solution
[tex]R = \frac {1}{\lim_{n\rightarrow\infty}\sqrt [n]{\frac {(1 + 2cos\frac {\pi n}{4})^n}{lnn}}} = \lim_{n\rightarrow\infty}\frac {e^{\frac {ln(lnn)}{n}}}{(1 + 2cos\frac {\pi n}{4})}[/tex]
In answers [tex]R=\frac{1}{3}[/tex].
[tex]\lim_{n\rightarrow\infty}e^{\frac {ln(lnn)}{n}} = 1[/tex].Then is
[tex]\lim_{n\rightarrow\infty}(1 + 2cos\frac {\pi n}{4}) = 3[/tex]?
As I know usually [tex]\lim_{x\rightarrow 0}cosx=1[/tex],not
[tex]\lim_{x\rightarrow\infty}cosx=1[/tex]