Find the radius of convergence, R, of the series. ?_{n=1}^{?} rac{n}{3^n}(x + 7)^n R = Find the interval, I, of the convergence of the series. (Enter your answer using interval notation.) I =
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Using the ratio test, we have: lim |(c + 7)" 3(n+1) / (c + 7)" 3n)| = lim |(c + 7)" 3| = |c + 7|" 3 Since the limit exists and is finite, the series converges absolutely for |c + 7| < 1. Therefore, the radius of convergence is R = 1. Show more…
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