[AP Calc] Unit 9: Series and Sequences

studied byStudied by 41 people
5.0(2)
Get a hint
Hint

partial sum

1 / 15

16 Terms

1

partial sum

knowt flashcard image
New cards
2

geometric series

|r|<1 → convergent

|r|≥1 → divergent

<p>|r|&lt;1 → convergent</p><p>|r|≥1 → divergent</p>
New cards
3

harmonic series

always divergent

<p>always divergent</p>
New cards
4

test for divergence

if the lim(a) DNE or lim(a)≠0 → the series is divergent

New cards
5

integral test

only used if the function is continuous, positive, and decreasing

take the integral, then the limit

New cards
6

p-series

p>1; convergent

p≤1; divergent

New cards
7

remainder estimate for the integral test

where is f continuous, positive, and decreasing for x≥n and Σa is convergent

<p>where is f continuous, positive, and decreasing for x≥n and Σa is convergent</p>
New cards
8

comparison test

if Σa and Σb are series with positive terms

<p>if Σa and Σb are series with positive terms</p>
New cards
9

limit comparison test

where c is positive and finite and Σa and Σb are series with positive terms

<p>where c is positive and finite and Σa and Σb are series with positive terms</p>
New cards
10

alternating series

a series whose terms alternate from positive to negative

<p>a series whose terms alternate from positive to negative</p>
New cards
11

alternating series test

knowt flashcard image
New cards
12

alternating series error bound theorem

knowt flashcard image
New cards
13

absolutely convergent

a series, Σa, is ______ if Σ|a| is convergent

New cards
14

conditionally convergent

a series, Σa, is ______ if Σ|a| is divergent

New cards
15

ratio test

knowt flashcard image
New cards
16

root test

knowt flashcard image
New cards

Explore top notes

note Note
studied byStudied by 10 people
... ago
5.0(1)
note Note
studied byStudied by 3666 people
... ago
4.4(12)
note Note
studied byStudied by 75 people
... ago
5.0(1)
note Note
studied byStudied by 71 people
... ago
5.0(2)
note Note
studied byStudied by 46 people
... ago
5.0(2)
note Note
studied byStudied by 30 people
... ago
4.0(2)
note Note
studied byStudied by 47 people
... ago
5.0(1)
note Note
studied byStudied by 12 people
... ago
5.0(1)

Explore top flashcards

flashcards Flashcard (135)
studied byStudied by 70 people
... ago
5.0(1)
flashcards Flashcard (25)
studied byStudied by 6 people
... ago
5.0(1)
flashcards Flashcard (48)
studied byStudied by 2 people
... ago
5.0(1)
flashcards Flashcard (33)
studied byStudied by 1 person
... ago
5.0(1)
flashcards Flashcard (73)
studied byStudied by 40 people
... ago
5.0(2)
flashcards Flashcard (39)
studied byStudied by 1 person
... ago
5.0(1)
flashcards Flashcard (37)
studied byStudied by 2 people
... ago
5.0(1)
flashcards Flashcard (292)
studied byStudied by 4 people
... ago
5.0(1)
robot