4) Find the interval of convergence and radius of convergence for $$ \sum_{n=0}^{\infty} \frac{(x-3)^{n+1}}{(n+1)4^{n+1}} $$. Test the endpoints of your interval to determine inclusivity.
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The power series is given by: $$ \sum_{n=0}^{\infty} \frac{(x-3)^{n+1}}{(n+1)4^{n+1}} $$ We will use the Ratio Test to find the radius of convergence. The Ratio Test states that a series $$ \sum a_n $$ converges if $$ \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} Show more…
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