# Shared Flashcard Set

## Details

Calculus III Final
Final Exam Drills
8
Mathematics
05/09/2017

Term
 What is the rule for Convergence and Divergence of a P-Series?
Definition
 [image]Convergent if P > 1Divergent if P [image] 1
Term
 When is a Geometric Series Convergent or Divergent?
Definition
 [image]Convergent |r| < 1Divergent |r| [image] 1
Term
 When can you use the Comparison Test?
Definition
 if an ≤ bn for all n, and ∑bn is convergent then ∑an is Convergent if  an ≥ bn for all n, and ∑bn divergent, then ∑an is divergent
Term
 What is the Divergence test? How do you use it?
Definition
 lim an ≠ 0 Then the ∑an is divergent
Term
 What is the Integral test?
Definition
 if ∫f(x)dx converges, then the series converges If it diverges then the series diverges
Term
 What is the Ratio Test?
Definition
 lim|(an+1)/(an)| if the lim >1 it is divergent if the lim < 1 it is convergent if the lim = 1 then the test is inconclusive
Term
 Alternating Series Test
Definition
 If for all n, an is positive, non-increasing (i.e. 0 < an+1 <= an), and approaching zero, then the alternating seriessum (1..inf) (-1)n an and sum (1..inf) (-1)n-1 anboth converge.If the alternating series converges, then the remainder RN = S - SN (where S is the exact sum of the infinite series and SN is the sum of the first N terms of the series) is bounded by |RN| <= aN+1
Term
 Root Test
Definition
 Let L = lim (n -- > inf) | an |1/n.If L < 1, then the series sum (1..inf) an converges.If L > 1, then the series sum (1..inf) an diverges.If L = 1, then the test in inconclusive.
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