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Unformatted text preview: (i) If lim = ∞ → c b a n n n then either both series converge or both series diverge. (ii) If lim = ∞ → n n n b a and ∑ n b converges, then ∑ n a also converges. (iii) If ∞ = ∞ → n n n b a lim and ∑ n b diverges, then ∑ n a also diverges. 6. Ratio Test Let ∑ n a be a positiveterm series, and suppose that L a a n n n = + ∞ → 1 lim (i) If 1 < L , the series is convergent (ii) If ∞ = + ∞ → n n n a a L 1 lim or 1 , the series is divergent. (iii) If 1 = L , apply a different test; the series may be convergent or divergent. 7. Root Test Let ∑ n a be a positiveterm series, and suppose that L a n n n = ∞ → lim (i) If 1 < L , the series is convergent (ii) If ∞ = ∞ → n n n a L lim or 1 , the series is divergent. (iii) If 1 = L , apply a different test; the series may be convergent or divergent....
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 Spring '08
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 Calculus, lim, positiveterm series

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