Which one of the following series diverges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$

B) $\sum _ { n = 1 } ^ { \infty } \left( \frac { \pi } { 4 } \right) ^ { n }$

C) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n + \ln n }$

D)$\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 4 } }$

E)None of these

Question

Which one of the following series diverges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$

B) $\sum _ { n = 1 } ^ { \infty } \left( \frac { \pi } { 4 } \right) ^ { n }$

C) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n + \ln n }$

D)$\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 4 } }$

E)None of these

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n + \ln n }$ diverges because it behaves like the harmonic series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n }$, which is known to diverge.

Which One of the Following Series Diverges? A) ∑n=1∞1n1.0001\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }∑n=1∞​n1.00011​

Which One of the Following Series Diverges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$