BC Calc III
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Quiz #4 Name:
You must show enough work so that I can recreate your results.
#1. Complete (no work necessary):
An expression of the form k

 a k
is called an .
Corresponding to this, we have the sequence { S n
}, which is called the
. The n th
term of this sequence is given by S n
= .
The sequence { a n
} is called .
If lim k
 a k

0 then .
An example of a divergent series n

 a n
with a
 n
0 is given by a
 n
#2. Determine the limit of each sequence. Write DNE if the limit does not exist. No work necessary. a.
n lim

1
  b.
n lim
 c.
n lim tan





1

 n
2 n
2

1




 d.
n lim






1

2 n
 n


BC CALC III

#3. Determine whether each series converges or diverges. Justify your answer carefully and completely a. n

3 n



2 n
3  n b.
n



1 n

3
3 n
BC CALC III

#3. (continued) Determine whether each series converges or diverges. Justify your answer carefully and completely c.
n



1


2 n  n !

 d.
n



1

 tan

1
1
 n
2 n


BC CALC III

#4. Evaluate each infinite series showing all work (or explain briefly why it diverges). a.
k



1
1

1 k k

2 b.
k



1

2
 k

2

#5. Find a value of n such that S approximates the value of the series n k

 1
with

1 k

3 k an error of at most .001. Explain carefully.
BC CALC III