Series test's Flashcards
Infinite series equals to a?
Finite sum or infinite sum
what does interval of convergence mean?
(domain of f(x))
how to find interval of convergence?
ratio test with |absolute value|
Divergence test
Limit as n approaches infinity a sub n doesn’t equal 0
p-series converges
P>1
p-series diverges
p
Geometric Series converges
|r|
Geometric Series Diverges
|r| > 1 series diverges
Comparison test
Compare using 1/n^p or Geometric Series.
Comparison test converges
Series smaller than a converger then series converges
Comparision Test diverges
Series larger than a diverger then series diverges
Limit comparison test
lim as n approaches a sub n/b sub n : use when a sub n is a rational function
Ratio Test converges
0
Ratio Test diverges
r > 1
Ratio test fails
r = 1
use ratio test when
there are factorials or when there is Geometric series with other stuff
root test converges
0
root test diverges
r > 1 diverges
r = 1
test fails
Alternating series first test
Check absolute convergence - any test
Alternating Series test (leibniz’s test) diverges if
diverges if the lim as n approaches infinity does not equal 0
