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.
Others have already explained why learning more languages makes you a better programmer.
As for convincing your boss it's worth it, this is probably just your company's culture.  Some places make career and skill progress a policy (move up or out), some places value it but leave it up to the employee's initiative, and some places are very focused on the bottom line.
If you have to explain why learning a language is a good thing to your boss, my advice would be to stay at work only as long as necessary, then go home and study new things on your own.
Why learn Perl, Python, Ruby if the company is using C++, C# or Java as the application language?