Which of the following series converges?
1) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { e ^ { n } }$
2) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { \sqrt { e ^ { n } } }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { \sqrt [ 3 ] { e ^ { n } } }$
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 series converges?
1) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { e ^ { n } }$ 
2) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { \sqrt { e ^ { n } } }$ 
3) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { \sqrt [ 3 ] { e ^ { n } } }$ 
A)None
B)1
C)2
D)3
E)1, 2
F)1, 3
G)2, 3
H)1, 2, 3

Quizplus · Accepted Answer

All three series converge because they are geometric series with a common ratio less than 1.

Which of the Following Series Converges? 1) ∑n=1∞1en\sum _ { n = 1 } ^ { \infty } \frac { 1 } { e ^ { n } }∑n=1∞​en1​

Which of the Following Series Converges?
1) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { e ^ { n } }$