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**Unformatted text preview: **b a If and b diverges then a diverges b →∞ →∞ →∞ = = = ∞ ∑ ∑ ∑ ∑ ∑ ∑ VI. Ratio Test : 1 * ( 1) , lim 1) 1 2) 1 3) 1 n n n n n a For a a Series converges if Series diverges if or Inconclusive if ρ + →∞-= < ∞ = ∑ VII. The nth-Root Test: ( 1) , lim 1) 1 2) 1 3) 1 n n n n n For a a Series converges if Series diverges if p or Inconclusive if →∞-= < ∞ = ∑ VIII. The Alternating Series: 1 1 2 3 4 1 1 * ( 1) ...... : 1) ' 2) 3) n n n n n n n For a a a a a converges if all three are satisfied The a s are all positive a a for all n a as n ∞ + = +-=-+-+ ≥ → → ∞ ∑...

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- Fall '05
- levy
- Geometric Series, Mathematical Series, series converges, series diverges