# Chapter 9 1 ```Chapter 9
1

 1 

 2
n 1  n 
Does
converge
or diverge and why?
2
n2



n 1  3n 

Does
converge
or diverge and why?
3

 sin n 

 5 

n 1  n
Does
converge
or diverge and why?
4

 1 
(1)  3


n

2


n 1
Does
converge
or diverge and why?
n
5

 1 
(1) 


n

4


n 1
Does
converge
or diverge and why?
n
6

2

 
n 1  3 
n
Does
converge
or diverge and why?
7
How can you tell if a
series is alternating?
8
When proving an
alternating series converges,
you first should…
9
You have shown an
alternating series does not
converge absolutely, how
do you show it converges
conditionally?
10
When is it a good time to
use the root test?
11
How do you prove a
series converges with the
root test?
12
How do you know if a
p-series diverges?
13
If you want to prove a
series converges using the
direct comparison test you
must…
14
The limit comparison test
can prove a series is a
convergent series if …
15
When is it a good time to
use the RATIO test?
What must happen for a
series to converge using
this test?
16
How do you find the
Interval of Convergence
of an infinite series?
17
How do you find a Taylor
polynomial approximation
around x = 0?
18
What is the general term of
the Taylor series centered
around zero for
2x
f ( x)  e
What are the first four
terms of the Taylor series
centered around zero for
1
f ( x) 
1 x
20
What is the general term of
the Taylor series centered
around zero for
f ( x)  cos x
21
State the first four terms of
the Taylor series centered
around zero for
2
f ( x)  sin x
22
What is the general term
of the Taylor series
centered around zero for
1
f ( x) 
1 x
23
```