Mathematics, 05.07.2021 19:40 kylemartinez13
Use the binomial series to expand the function as a power series. Find the radius of convergence. x/ â 9+ x^2
Answers: 1
![\implies \dfrac{x}{3}\Bigg [ 1 + (-\dfrac{1}{2})*(\dfrac{x^2}{9})+ \dfrac{(-\dfrac{1}{2})(-\dfrac{1}{2}-1)}{2!}(\dfrac{x^2}{9}) ^2 + \dfrac{(-\dfrac{1}{2})(-\dfrac{1}{2}-1) (-\dfrac{1}{2}-2)}{3!} ) (\dfrac{x^2}{9}) ^3+ ... \Bigg ]](/tpl/images/1389/3563/b66ec.png)
![= \dfrac{x}{3}\Bigg [ 1 - \dfrac{x^2}{18}+ \dfrac{3}{5832}*\dfrac{x^4}{1}-\dfrac{15}{34992}x^6+... \Bigg ]](/tpl/images/1389/3563/d3623.png)
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Use the binomial series to expand the function as a power series. Find the radius of convergence.
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