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
- 3rd side (hint)
|
Geometric Series
|
Summation 0 to infinity of a*r^k
|
Converges to a/(1-r) if abs(r)<1
|
|
|
kth Term Test
|
All series
|
if limit of asubk as k approaches infinity doesn't equal zero, it diverges
|
|
|
Integral Test
|
Summation from 1 to inf. of asubk where asubk is some continuous function of k, decr, and always greater than zero
|
the summation and the integral of f(k) on the same interval either both converge or both diverge
|
|
|
p-Series Test
|
The one with 1/k^p
|
Converges for p>1, diverges for p> or = 1
|
|
|
Comparison Test
|
you have 2 summations, where one nth term is always greater than the other
|
If the greater one converges, the lesser one converges. If the lesser one diverges, the great one diverges.
|
|
|
Limit Comparison Test
|
2 summations, both nth terms are greater than zero, and the limit of one over the other is greater than zero
|
Both Converge or both diverge
|
|
|
Absolute Convergence
|
Series with some positive and negative terms(including alternating series)
|
if abs of summation converges, then the summation converges absolutely
|
|
|
Ratio Test
|
Any series
|
limit as k approaches inf. of abs(asub(k+1)/asubk)
If it's less than 1 Converges If it's greater than 1 Diverges |
|
|
Root Test
|
Any series
|
kth root of abs of asubk
|
