Determine which one of the p-series below is divergent.
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 03 } }$
B) $\sum _ { n = 1 } ^ { \infty } n ^ { - 4 x }$
C) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 3 e } }$
D) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 4 } }$

Question

Quizplus · Accepted Answer

A p-series of the form $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { p } }$ converges if and only if p > 1. In this case, p = 3, which is less than 1, so the series diverges. Therefore, option A is the best choice as it is the only divergent p-series given.

Determine Which One of the P-Series Below Is Divergent ∑n=1∞1n03\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 03 } }∑n=1∞​n031​

Determine Which One of the P-Series Below Is Divergent $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 03 } }$