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18 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Sequence |
A list of numbers |
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Convergence of a Sequence |
Doesn't approach a number: diverges. Approaches 0: converges to 0. |
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Series |
The sum of a list of numbers. |
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Convergence of a Series |
Equals infinity: Diverges Anything else: You must do a test to find out. |
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Geometric Series |
Multiply to get the next term. |r|<1 it converges. |r|=>1 it diverges. |
What is the sum if it converges? |
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Telescoping Series |
Back (Definition) |
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P-series |
Back (Definition) |
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Divergence Test (Nth Term Test) |
Condition for Convergence: There is none. Condition for Divergence: Limit does not equal 0. |
Use this test first. When lim=0, use another test. |
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Integral Test |
If integral of f(x) < infinity: Then series converges. If integral of f(x) does not exist: Then series Diverges |
The value of the integral does not equal the value of the series. |
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P-test |
If p>1: Series converges. If p<=1: Series diverges. |
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Ratio Test |
Ans <1: It converges Ans >1: It diverges Ans =1: Inconclusive; use another test. |
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Root Test |
Ans <1: Converges Ans >1 or infinity: Diverges Ans =1: Inconclusive, use another test. |
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Limit Comparison Test |
0k / bk k converges: Series Converges. Lim ak / bk > 0 and bk diverges: Series Diverges. |
Always compare to a p-series. Use when you have a polynomial in the denominator and numerator ( or just denominator). |
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Direct Comparison Test |
You compare the series you are testing to one you know to determine if it converges or diverges. If An is <= bn :Then An converges. If An is => bn : Then An diverges too. |
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Alternating Series |
The signs of the terms alternate from positive to negative. If lim An = 0, then series converges. If lim An does not equal 0, then series diverges. |
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Absolute Convergence |
The series converges w/ negative signs and w/o. |
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Conditional Convergence Test |
The series does not converge with negative signs and without. |
Usually use p-series with this. |
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Power Series |
A series with a variable "x". Ck and "a" are real numbers. |
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