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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 nthRoot 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

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