Unformatted text preview: ± k (1 + 1 /k ) k ² k = | x | lim k →∞ ± 1 + 1 k ² k = e | x | This means that the series converges when e | x | < 1, that is, when | x | < 1 /e . This means the radius of convergence is 1 /e . NOTE: In particular, this means that when x = 1, the ratio test gives e as the limit and so ∑ ∞ k =1 k k k ! does NOT converge. For those of you that I talked to today, this means you can’t just do a comparison test with this series in problem 1 (since it is less than something that diverges the comparison does not give you any information). 1...
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- Fall '07