Consider the Two Series: (A) $\sum _ { k = 2 } ^ { \infty } \frac { \ln k } { k }$

question 40

Essay

Consider the two series: (a) $\sum _ { k = 2 } ^ { \infty } \frac { \ln k } { k }$ and (b) $\sum _ { k = 2 } ^ { \infty } \frac { 1 } { k \ln k }$ . Suppose you compare (a) and (b) to the series $\sum _ { k = 1 } ^ { \infty } \frac { 1 } { k }$ . What (if anything) can you conclude about the convergence or divergence of (a) and (b) using only the Comparison Test?