Using #inject to join strings from an array

There are better ways then #inject, see the other answers. But if you insist you could just String#rstrip the trailing space character.

Or turn the block around and check whether memo is empty before adding the character.

memo << " " unless memo.empty?
memo << name.capitalize

I'm not sure about the << operator. I would use +, but that is probably just be a personal preference.

a = ["emperor", "joshua", "abraham", "norton"]
a.drop(1).inject(a.first.capitalize){|res,m| res << ' '+m.capitalize }

Try this:

a.map{|t| t.capitalize}.join(" ")

I don't think you can escape from the extra space with inject. Also you need to do

memo = memo + word.capitalize + " " 

EDIT: as the statement has changed to force you not to use join and map, here is a bit ugly solution with inject:

a.inject("") do |memo, world|
  memo << " " unless memo.empty?
  memo << word.capitalize
end