Series Tests Flashcards
memorize
1
Q
Ratio Test Converges
A
lim |a(n+1)/a(n)| < 1
x–>infinity
2
Q
Ratio Test Diverges
A
lim|a(n+1)/a(n)| > 1
x–> infinity
3
Q
Geometric Series Converges
A
a(n) = r^n and |r| < 1
4
Q
Geometric Series Diverges
A
|r| > 1
5
Q
P-series converges
A
p > 1
6
Q
P-series diverges
A
p < 1
7
Q
integral test converges
A
positive, decreasing, continuous
8
Q
Alternating Series Test
A
a(n) is alternating
and |a(n)| decreases to 0
9
Q
Nth term test converges
A
lim a(n) = 0
n –> infinity
10
Q
Nth term test diverges
A
lim a(n) does not equal 0
11
Q
Limit Comparision
A
Compare to geometric/p-series
12
Q
Telescoping Series
A
partial fractions
13
Q
Geometric Sum
A
ar^n = ar^k/1-r
14
Q
Polar Area
A
A = 1/2 intergral [r^(theta)}^2
15
Q
Polar Parametric
A
x = r(theta)(cos(theta)) & y=r(theta)(sin(theta))
