Robert
The <servlet-name> and <jsp-file> tags in the deployment descriptor already serve as a mapping from the Servlet name you enter in the browser to the location of the JSP file.
The <servlet-mapping> tag is used to determine which URL
patterns should be handled by which servlet, and should not be required by the code you supplied earlier in this post.
I've tried it out using Tomcat without servlet mappings and it definitely does work.
Maybe I'm just lucky