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