Which of the following series converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { n } { 2 + 3 n } \right) ^ { n }$
2) $\sum _ { n = 2 } ^ { \infty } \frac { n + 1 } { \sqrt { n ^ { 4 } - 1 } }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 1 + n ^ { 2 } }$
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) $\sum _ { n = 1 } ^ { \infty } \left( \frac { n } { 2 + 3 n } \right) ^ { n }$ 
2) $\sum _ { n = 2 } ^ { \infty } \frac { n + 1 } { \sqrt { n ^ { 4 } - 1 } }$ 
3) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 1 + n ^ { 2 } }$ 
A)None
B)1
C)2
D)3
E)1, 2
F)1, 3
G)2, 3
H)1, 2, 3

Quizplus · Accepted Answer

1) Converges by the Ratio Test.3) Converges by the Integral Test.

Which of the Following Series Converges? 1) ∑n=1∞(n2+3n)n\sum _ { n = 1 } ^ { \infty } \left( \frac { n } { 2 + 3 n } \right) ^ { n }∑n=1∞​(2+3nn​)n

Which of the Following Series Converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { n } { 2 + 3 n } \right) ^ { n }$