![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}](/tpl/images/0345/0448/c1f9d.png)
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}](/tpl/images/0345/0448/3cdc1.png)
![\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}](/tpl/images/0345/0448/2a9a0.png)
, you have 
, which means you end up with
so that 
is the ROC. You get
Find the radius of convergence and the internval of convergence:
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Mathematics, 24.10.2019 22:43 ijohnh14
Find the radius of convergence and the internval of convergence:
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