___________________________________________________________
Calculus II Quiz
#7 April
29, 2005
Name_________________ R. Hammack Score
______
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Decide if the following series converge or diverge. In the case of convergence
state the sum, if possible.
(1) (
-
)
=
=
(
-
)
= 3-0 = 3
Note, this is a telescoping series, since:
=
(
-
)
+ (
-
)
+ (
-
)
+ (
-
)
+...+ (
-
)
=
-
(2)
+
+
+
+
+
+
...
Geometric series with a =and
r =
<
1.
CONVERGES to =
=
=
(3)
+
+
+
+
+
+
... = 5(
+
+
+
+
+
+
...)
Harmonic series with first 6 terms deleted. DIVERGES
(4)
+
+
+
+
+
+
...
P-series with p = 4 > 1. CONVERGES
(5)
+
+
+
+
+
+
...
P-series with p = 1/2 < 1. DIVERGES