Does the series converge if Sn = 5 - 1/n?

[KTiaam]

Homework Statement

The nth partial sum of the series
∞
Ʃ a_n
n=1


is given S_n = 5-1/n


Determine weather the series is convergent or divergent

The Attempt at a Solution

Looked in my book on how to do this one.
couldn't find anything on it.

What i was thinking was find the sum of all n's and finding a pattern and use that as a_n
however it didnt work, so I am stuck.

 

[Dick]

Homework Statement

The nth partial sum of the series
∞
Ʃ a_n
n=1


is given S_n = 5-1/n


Determine weather the series is convergent or divergent

The Attempt at a Solution

Looked in my book on how to do this one.
couldn't find anything on it.

What i was thinking was find the sum of all n's and finding a pattern and use that as a_n
however it didnt work, so I am stuck.

The sum of the series is DEFINED to be the limit of the partial sums. There's not much else to know. What is it?