Partition Function For a Single Molecule

[conorod]

Homework Statement

Polymers, such as rubberbands, are made of very long molecules, usually
tangled up in a configuration that has lots of entropy. As a very crude
example of a rubber band, consider a chain of N molecules which we call
links, each of length l. Imagine that each link has only two possible states,
pointing either left or right. If a link point to the right, it has energy −lF,
where F > 0 is the force pulling on the rubber band. If a link points to the
left, it has energy +lF. The end-to-end length of the rubber is
L = (<NR> − <NL>)l ,
where <NR> and <NL> are the average number of links that point to the right
and to the left, respectively.
(i) Write the partition function for a single link (molecule), Z1.

The Attempt at a Solution

Since I did this out in microsoft word I attached a screenshot of what I think is the solution - partition functions are not my strong point and I have an exam tomorrow where I believe a similar question will come up, so I just want to check if I have the correct answer.

 

[TSny]

That looks right to me.