Page 270 - Calculus Workbook For Dummies

254 Part IV: Integration and Infinite Series

3 n 1 1. The nth term converges to zero.
Q. !^ - 1h
n 1 n lim 1 = 0
=
A. The series is conditionally convergent. n " 3 n
If you make this a series of positive 2. The terms are non-increasing.
1
terms, it becomes a p-series with p = , The series is thus conditionally
which you know diverges. Thus, the 2 convergent.
above alternating series is not absolutely
convergent. It is, however, conditionally
convergent because it obviously satisfies
the two conditions of the alternating
series test:

3 n 1 n + 1 3 n n + 1
+
21. !^ - 1h *22. !^ - 1h 2
n 1 3 n + 1 n 3 n - 2
=
=
Solve It Solve It