# Shared Flashcard Set

## Details

11.7 Tests for Convergence or Divergence
11.7 Tests for Convergence or Divergence
10
Mathematics
04/10/2015

Term
 The form Σ1/np should be used with which test?
Definition
 The p-series test
Term
 If the series has the form ∑arⁿ or ∑arⁿ-1 which test should be used?
Definition
 It's a geometric series so: a/1-r  If |r|<1 convergent If |r|≥1 divergent
Term
 Two notes for comparison test:
Definition
 1. If Σbn is convergent and an≤bn then Σanconvergent   2. If Σbn is divergent and an≥bn then Σandivergent
Term
 Equation and rules (2) for limit comparison test
Definition
 lim n→∞ an ⁄bn = c 1. C must be finite & greater than 0 2. If so, both series are convergent or both series are divergent.
Term
 What test should be used for limn→∞ an ≠0?
Definition
 The test for divergence should be used (if limn→∞ an ≠0 or DNE then series divergent)
Term
 What test should be used for the form ∑(-1)nbn ? What are the requirements for convergence?
Definition
 Alternating Series Test  If bn+1 ≤bn & the limn-->∞=0 then the series converges
Term
 If a series involves a fraction or a constant raised to the nth power, what test should be used?
Definition
 The ratio test |an+1/ an|
Term
 Three rules for ratio test:
Definition
 1) if L <1 absolutely convergent 2) if L>1 or ∞ then divergent 3) If L=1 no conclusion
Term
 If the series is in the form of (∑an)n what test should be used?
Definition
 Root test  (Same rules for ratio test)
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