Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
9 Cards in this Set
- Front
- Back
|
Divergence Test
|
DIVERGENCE TEST:
let L = limit(An) as n approaches infinity L not equal to zero: series DIV L equal to zero: inconclusive; necessary/not sufficient |
|
|
Integral Test
|
INTEGRAL TEST:
Create function f(x) by replacing n-terms with x-terms, then integrate The result and the series ACT together, they are not necessarily the same value. *Use when f(x) is easy to integrate |
|
|
Comparison Test
|
COMPARISON TEST:
Pick a series Bn for comparison such that An is less than or equal to Bn at all times If Bn converges: An converges Similarly, if An diverges, Bn diverges *Use as last resort *NOT ON THE QUIZ |
|
|
Limit-Comparison Test
|
LIMIT-COMPARISON TEST:
Pick a series Bn for comparison: let L = limit (An/Bn) as n approaches infinity If 0 < L < infinity, then An and Bn ACT together Special cases: L = 0 and Bn converges, then An converges L = infinity and Bn diverges, then An diverges |
|
|
Ratio Test
|
RATIO TEST:
Let L = limit |An+1 / An| as n approaches infinity Invert/multiply/reduce, etc... L < 1: Convergent L > 1: or L = infinity: Divergent L = 1: inconclusive ^same criteria as root test *Use with factorials or nth powers |
|
|
Root Test
|
ROOT TEST:
Let L = limit |An|^(1/n) as n approaches infinity L < 1: Convergent L > 1: or L = infinity: Divergent L = 1: inconclusive ^same criteria as ratio test *Try this test when An has nth powers |
|
|
Alternating Series Test (AST)
|
AST:
Let L = limit (An) as n approaches infinity (without alternator part) L = 0: Convergent L not 0: Divergent *Only for alternating series (duh) |
|
|
Geo Series
|
Form: a(r)^n
If |r| >= 1: diverges if |r| < 1: converges to a / (1-r) |
|
|
P series
|
Form: 1 / n^p
p <= 1: diverges p > 1: converges |
