Difficult# Diverging Series

APCALC-UEUBEK

Determine which series diverge:

I.$\ \ \ \sum _{ n=1 }^{ \infty }{ \cfrac { \sqrt { { n }^{ 2 }+5 } }{ n } } $

II.$\ \ \sum _{ n-1 }^{ \infty }{ \cfrac { 2 }{ n( n+2 ) } } $

III.$\ \sum _{ n=0 }^{ \infty }{ { e }^{ n } } $