AP Calculus BC
Series
Quick Quiz Version 1
1.
2.
Name __________________
List the first four terms and the general term for each Maclaurin Series.
a.
1
=
1− x
_________________________________
b.
1
=
1+ x
_________________________________
c.
ex =
_________________________________
d.
sin x =
_________________________________
e.
cos x =
_________________________________
f.
ln(1 + x) =
_________________________________
g.
tan −1 x =
_________________________________
Error Analysis
a.
Alternating Series Error Bound
If ___________________________ and _______________________,
then we approximate its sum with the nth partial sum, and the error does
not exceed ________________.
b.
Lagrange Error Bound Formula
_____________________________
3.
The Taylor Series for f at x = a is given by:
________________________________________________________________
4.
Tests for Convergence of a Series
nth term test for divergence If lim an  0 then
n→

p-series test
1
 np

 an
_____________.
n =1
converges if __________ and diverges if __________.
n=1

 ar n−1 = a + ar + ar 2 + ar 3 +
geometric series test
converges iff __________.
n=1
The sum of the series is _____________.
An alternating series will converge if the following conditions
alternating series test
are met: ___________________________________________
___________________________________________________.
Given: 0  an  bn for all n.


If
direct comparison test
 bn
_____________, then
If
 an
_____________, then
n =1
 an
_______________.
n =1

n =1

 bn _______________.
n =1
Suppose that an  0 and bn  0 for all n  0 . Define c =_________.
limit comparison test
If c is _____________ and _____________, then either
_______________________ or ______________________ .
integral test
If f ( x ) is ____________________________________, then

 f ( n ) converges iff _______________________________.
n=1

If ________________________, then
ratio test
 an
converges.
 an
diverges.
n =1

If ________________________, then
n =1
If ________________________, then the test is inconclusive.