Question

prove divergence

Answer 1

\[\huge \color{red}{\sum_{k=0}^\infty \frac{ 1 }{ k^{(1+\frac{ 1 }{ k })} }}\]

Answer 2

i notice that\[\lim_{x \rightarrow \infty}x^{1/x}=1\]

Answer 3

Use Summation of series

Answer 4

since we have\[\frac{ 1 }{ k }\frac{ 1 }{ k^{\frac{ 1 }{ k }}}\]

Answer 5

what is that summation of series can you pls explain

Answer 6

google Raabe criterion and apply