This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**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 positive-term 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 positive-term 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....

View
Full Document

- Spring '08
- varies
- Calculus, lim, positive-term series