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.
I primarily program in Java and C# but use dynamic languages (ruby/perl) to support smoother deployment, kicking off OS tasks, automated reporting, some log parsing, etc.
After a short time learning and experimenting with ruby or perl you should be able to write some regex manipulating scripts that can alter data formats or grab information from logs.   An example of a small ruby/perl script that could be written quickly would be a script to parse a very large log file and report out only a few events of interest in either a human readable format or a csv format. 
Also, having experience with a variety of different programming languages should help you think of new ways to tackle problems in more structured languages like Java, C++, and C#.
Why learn Perl, Python, Ruby if the company is using C++, C# or Java as the application language?