Use the Integral Test to Show That the Series $\sum _ { k = 2 } ^ { \infty } \frac { 1 } { k ( \ln k ) ^ { y } }$

Essay

Use the integral test to show that the series $\sum _ { k = 2 } ^ { \infty } \frac { 1 } { k ( \ln k ) ^ { y } }$ converges if $p > 1$ and diverges if $p \leq 1$ .Hint: Consider the two cases $p = 1$ and $p \neq 1$ .