I just installed Raspian Jessie lite date 4-10-17. All articles state the username and password are "pi" and "rasberry". These do not work. What is the correct user and password?
The username is "pi" and the password is "raspberry", you have misspelled the word "raspberry" by missing the p.
If you still have issues, I would try re-downloading, re-formatting, and doing it once more. I think you'll be fine after correcting the password entry.
It's good practice after logging in to change the password of the user from the default.
Some users like to disable the pi account (especially if opened up to the internet) and create a new account and password to create minor security through obscurity, but it's not a replacement for following proper security practices.
If you are talking about root's password, its not set by default. Although whenever you write
su - it asks for root password. It shouldn't ask in the first place if there isn't any.
So in order to solve this, write in terminal
sudo passwd root and it will ask you twice to write password and you are good to go.