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What is the rule for Convergence and Divergence of a PSeries? 

Definition
[image] Convergent if P > 1 Divergent if P [image] 1 


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When is a Geometric Series Convergent or Divergent? 

Definition
[image] Convergent r < 1 Divergent r [image] 1 


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When can you use the Comparison Test? 

Definition
if a_{n} ≤ b_{n }for all n, and ∑b_{n} is convergent then ∑a_{n} is Convergent
if a_{n }≥ b_{n} for all n, and ∑b_{n} divergent, then ∑a_{n} is divergent 


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What is the Divergence test? How do you use it? 

Definition
lim a_{n} ≠ 0 Then the ∑a_{n} is divergent 


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What is the Integral test? 

Definition
if ∫f(x)dx converges, then the series converges
If it diverges then the series diverges 


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Definition
lim(a_{n+1})/(a_{n})
if the lim >1 it is divergent
if the lim < 1 it is convergent
if the lim = 1 then the test is inconclusive 


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Definition
If for all n, an is positive, nonincreasing (i.e. 0 < an+1 <= an), and approaching zero, then the alternating series sum (1..inf) (1)n an and sum (1..inf) (1)n1 an both 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 


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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. 

