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'Litov's Mean Value Theorem' printed from http://nrich.maths.org/
What happens if you reverse the two original numbers?
Try starting with $2, 8$ instead of $8, 2$.
What happens if you keep one of the starting numbers constant and
only change the other?
It might be faster to use a spreadsheet or to write a short program
to help you identify the limiting value (the value you get if you
continue this process indefinitely).
Keep a record of your results.
Share your results.
Test out your ideas.