Which of the following are alternating series?
1) $\frac { ( - 1 ) ^ { 2 n } } { n }$
2) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { n }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { \cos n \pi } { n }$
A)None
B)1
C)2
D)3
E)1, 2
F)1, 3
G)2, 3
H)1, 2, 3

Question

Which of the following are alternating series?
1) $\frac { ( - 1 ) ^ { 2 n } } { n }$ 
2) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { n }$ 
3) $\sum _ { n = 1 } ^ { \infty } \frac { \cos n \pi } { n }$ 
A)None
B)1
C)2
D)3
E)1, 2
F)1, 3
G)2, 3
H)1, 2, 3

Quizplus · Accepted Answer

2) and 3) are alternating series. In 2), the term $(-1)^{n-1}$ alternates sign for each successive value of $n$, making it an alternating series. In 3), $\cos(n\pi)$ alternates between 1 and -1 for each integer value of $n$, also creating an alternating series. 1) is not an alternating series because $(-1)^{2n}$ is always positive, making the series not alternate in sign.

Which of the Following Are Alternating Series? 1) (−1)2nn\frac { ( - 1 ) ^ { 2 n } } { n }n(−1)2n​

Which of the Following Are Alternating Series?
1) $\frac { ( - 1 ) ^ { 2 n } } { n }$