Mathematics, 08.12.2020 14:00 adrianvigil6400
Find a power series representation for the function. (Assume a > 0.) (Give your power series representation centered at x = 0.) f(x) = x5 a6 − x6
Answers: 1
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geometric series with 
![= \frac{\frac{x^5}{a^8}}{1+(\frac{x}{a})^8} \\\\ = \frac{x^5}{a^8} [ 1+ (\frac{x}{a})^8 + ((\frac{x}{a})^8)^2+.......]\\\\= \frac{x^5}{a^8} \sum_{\infty}^{n=0} (\frac{x}{a})^{8n}\\\\ = \sum_{\infty}^{n=0} (\frac{x^{8n+5}}{a^{8n+8}})\\\\a_n =(\frac{x^{8n+5}}{a^{8n+8}})](/tpl/images/0960/5035/fb44a.png)
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Find a power series representation for the function. (Assume a > 0.) (Give your power series repr...
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