Are the geometric, harmonic, and collapsing series all the same?

Or can i only test the geometric series by this formula: a/(1-r)

is it that the harmonic series ALWAYS diverges.

Is this because it continues on infinitly?

and the collapsing series, In order to determine if it converges, must i first put the equation in a two fractions form, through partial fraction substitution for example?

If i need to show specific problem examples i can, any further explanation to my questions can help. Just using basic calculus 3 skills here. thankyou.