Styling each page in multiple page posts differently?

I’m using the build in capability of dividing a post into multiple pages but would like to style the first page just like any singple post page but then the other pages differently.

The reason for this is that we use the excerpt as an introduction to each article which makes it confusing when you’re on the next page and that introduction shows up again.
See http://www.csripraktiken.se/2008/08/21/med-ett-gront-oga-for-lonsamhet/2/

If you can’t style them differently, is there a way of using if-commands such as on a traditional archive page? If this is a weekly archive, show this, if this is amonthly archve, show that etc.
– Which string should you then use to check that this isn’t the firt page of a multiple page post?