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)
![Underoverscript[∑ , k = 1, arg3]](HTMLFiles/Q7S05D_1.gif){kind=small}
(
-
)
= ![Underscript[lim , n∞]](HTMLFiles/Q7S05D_4.gif){kind=small}
= ![Underscript[lim , n∞]](HTMLFiles/Q7S05D_6.gif){kind=small}
(
-
)
= 3-0 = 3Note, 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