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Stewart_Calc_7ET ch11sec01
MULTIPLE CHOICE
1. Find the value of the limit of the sequence defined by
.
a.
b.
c.
d.
e.
2. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a.
b.
–5
c.
d.
Diverges
3. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a.
1
b.
c.
0
d.
Diverges
4. Determine whether the sequence converges or diverges. If it converges, find the limit.
a.
b.
c.
diverges
d.
e.
5. Find the value of the limit for the sequence given.
a.
b.
c.
d.
e.
6. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a.
13
b.
5
c.
Diverges
d.
–3
7. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a.
Diverges
b.
1
c.
d.
0
8. If $600 is invested at interest, compounded annually, then after n years the investment
is worth dollars. Find the size of investment after 7 years.
a.
$430.21
b.
$1,860.81
c.
$1,230.81
d.
$789.56
e.
$1,321.06
MULTIPLE RESPONSE
1. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the
sequence bounded?
a.
increasing
b.
decreasing
c.
not monotonic
d.
bounded
2. Which of the following series is convergent?
a.
b.
c.
NUMERIC RESPONSE
1. Find a formula for the general term of the sequence, assuming that the pattern of the
first few terms continues.
2. Determine whether the sequence converges or diverges. If it converges, find the limit.
3. Determine whether the sequence defined as follows is convergent or divergent.
4. Find the value of the limit for the sequence.
5. Find the exact value of the limit of the sequence defined by .
6. The terms of a series are defined recursively by the equations .
Determine whether converges or diverges.
SHORT ANSWER
1. Write the first five terms of the sequence whose term is given.
2. Determine whether the sequence defined by
converges or diverges. If it converges, find its limit.
3. Determine whether the sequence defined by
converges or diverges. If it converges, find its limit.
4. Find an expression for the term of the sequence. (Assume that the pattern continues.)
5. Graph the sequence defined by
.
Use the graph to guess at the convergence or divergence of the sequence.
6. An annuity is a sequence of payments made at regular intervals. Suppose that a sum of $200
is deposited at the end of each month into an account earning interest at the rate of 12% per
year compounded monthly. Then the amount on deposit at the end of the month is
.
Consider the sequence defined by
(a) Find the term of the sequence, and interpret your result.
(b) Evaluate and interpret your result.
