exam 3 Flashcards
1
Q
geometric series test
A
-1 < r < 1 = convergent
divergent otherwise
2
Q
alternating series test
A
- b1 > b2 > b3 > b4
- lim n-> ∞ bn = 0
3
Q
lim n-> ∞ (1+k/n)^n/k = ?
A
e
4
Q
ln(0) = ?
A
-∞
5
Q
test for divergence
A
if Σan does not equal 0 then Σan is divergent (don’t know if it’s convergent or not)
6
Q
p-series test
A
Σ1/n^p
p > 1 -> convergent
p < or equal to 1 -> divergent
7
Q
if Σ|an| is convergent…
A
the original series is absolutely convergent
8
Q
ratio test
A
lim n -> ∞ |an+1/an| = L
L < 1 -> Σan is A.C.
L > 1 -> Σan is divergent
L = 1 use other tests
9
Q
root test
A
lim n -> ∞ n√|an| = L
L < 1 -> Σan is A.C.
L > 1 -> Σan is divergent
L = 1 use other tests
10
Q
limit comparison test
A
an/bn cannot be 0 or ∞
if so, either are divergent or convergent
11
Q
t/f: n! > 2^n
A
true
