I wonder why would a C++, C#, Java developer want to learn a dynamic language?
Assuming the company won't switch its main development language from C++/C#/Java to a dynamic one what use is there for a dynamic language?
What helper tasks can be done by the dynamic languages faster or better after only a few days of learning than with the static language that you have been using for several years?
Update
After seeing the first few responses it is clear that there are two issues.
My main interest would be something that is justifiable to the employer as an expense.
That is, I am looking for justifications for the employer to finance the learning of a dynamic language. Aside from the obvious that the employee will have broader view, the
employers are usually looking for some "real" benefit.
Given the increasing focus to running dynamic languages (da-vinci vm etc.) on the JVM and the increasing number of dynamic languages that do run on it (JRuby, Grrovy, Jython) I think the usecases are just increasing. Some of the scenarios I found really benifited are

Prototyping- use RoR or Grails to build quick prototypes with advantage of being able to runn it on the standard app server and (maybe) reuse existing services etc.
Testing- right unit tests much much faster in dynamic languages
Performance/automation test scripting- some of these tools are starting to allow the use standard dynamic language of choice to write the test scripts instead of proprietary script languages. Side benefit might be to the able to reuse some unit test code you've already written.
Why learn Perl, Python, Ruby if the company is using C++, C# or Java as the application language?