Find the radius of convergence, R, of the series. ∑ n = 1 to ∞ x^6n/n! R = Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =
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Step 1
Using the ratio test, we have: lim n→∞ |(x^6(n+1))/(n+1)!| / |(x^6n)/n!| = lim n→∞ |x^6/(n+1)| = 0 Since the limit is less than 1 for all values of x, the series converges for all x. Therefore, the radius of convergence is infinity, R = ∞. Show more…
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