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.
Edit: I wrote this before reading the update to the original question. See my other answer for a better answer to the updated question. I will leave this as is as a warning against being the fastest gun in the west =)
Over a decade ago, when I was learning the ways of the Computer, the Old Wise Men With Beards explained how C and C++ are the tools of the industry. No one used Pascal and only the foolhardy would risk their companies with assembler.
And of course, no one would even mention the awful slow ugly thing called Java. It will not be a tool for serious business.
So. Um. Replace the languages in the above story and perhaps you can predict the future. Perhaps you can't. Point is, Java will not be the Last Programming Language ever and also you will most likely switch employers as well. The future is charging at you 24 hours per day. Be prepared.
Learning new languages is good for you. Also, in some cases it can give you bragging rights for a long time. My first university course was in Scheme. So when people talk to me about the new language du jour, my response is something like "First-class functions? That's so last century."
And of course, you get more stuff done with a high-level language.
Why learn Perl, Python, Ruby if the company is using C++, C# or Java as the application language?