Use the Ratio Test to determine the radius of convergence of [ sum_{n=1}^{infty} frac{x^{n}}{sqrt[5]{n} cdot 7^{n}} ]
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The Ratio Test states that for a series ∑a_n, the series converges if the limit as n approaches infinity of |a_(n+1)/a_n| is less than 1, diverges if the limit is greater than 1, and is inconclusive if the limit equals 1. In this case, our a_n is (x^n)/(n^(1/5) * Show more…
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Find the radius of convergence and interval of convergence for the given power series (note you must also check the endpoints). (Use inf for +∞ and -inf for -∞. If the radius of convergence is infinity, then notice that the infinite endpoints are not included in the interval). Radius of convergence: For the interval of convergence (1) the left endpoint is x= left end included (enter yes or no): (2) the right endpoint is x= right end included (enter yes or no): Using interval notation give the interval of convergence Help Sheet: Entering answer with interval notation
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