Math 9C
Final exam Study guide
C. Pro  Fall 2011
1
Concept questions
What is the difference between a sequence and a series?
Can you give the definition of what it means for a sequence to converge?
What is the definition for a series to converge?
If the
a
k
’s are nonnegative, why does this say the sequence of partial sums is an
increasing sequence?
What is the Monotone bounded convergence theorem?
Can you explain how the integral test is used to show your sequence of partial sums
is bounded?
How did we come up with the
p
test?
How are the integral test and the comparison test similar?
1.1
Sample Problems
State the integral test, comparison test, limit comparison test, alternating series test,
ratio test, and root test.
Find the
n
th term of the sequence
{
1
,
0
,
1
,
0
,
1
,
0
, . . .
}
Find the limits as
n
→ ∞
of the following sequences
• {
3
1
/n
}
• {
4
n
2
+2
n
3
+3
}
• {
1
2
n
}
• {
n
√
n
}
Hint:
n
√
n
=
e
ln(
n
)
n
(Do you know why?)
• {
n
sin
1
n
}
• {
n
ln
(
1 +
1
n
)
}
Hint: L’Hospital’s rule.
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 Fall '11
 c
 Math, Mathematical Series, 2k, 0 k, 4k

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