Moderate# Which Are Convergent Series?

APCALC-EYV9QE

Which of the following series converge?

I.$ \sum _{ n=1 }^{ \infty }{ { \left( \cfrac { \pi }{ 2e } \right) }^{ n } } $

II.$ \sum _{ n=1 }^{ \infty }{ \cfrac { { 2 }^{ n } }{ n! } } $

III.$ \sum _{ n=1 }^{ \infty }{ \cfrac { 1 }{ \sqrt { n } } } $