166 SCW, 11.5: Examples of Series That Have Both Negative and Positive Terms:

Example1(AlternatingHarmonicSeries):
∞
∑
k=1
k+1
(-1)
1
k
=1-
1
2
+
1
3
-
1
4
+...

Example2:
∞
∑
k=1
k+1
(-1)
2/k

=
2/1

-
2/2

+
2/3

-
2/4

+...

Example4(a):
∞
∑
k=1
k+1
(-1)
k+1
1
2
=
1
2
-
2
1
2
+
3
1
2
-
4
1
2
+...

Example4(a)(AbsoluteValueofEachTerm):
∞
∑
k=1

k+1
(-1)
k+1
1
2
=
1
2
+
2
1
2
+
3
1
2
+
4
1
2
+...

Example5:
∞
∑
k=1
Sin[k]
3
k
=
Sin[1]
1
+
Sin[2]
8
+
Sin[3]
27
+...