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    (Original post by UCASLord)
    Let f(n) be a function, defined for any integer n <= 0 as follows:

    1 if n = 0
    f(n) = (f(n/2))^2 if n > 0 and and n is even
    2f(n-1) if n > 0 and n is odd

    What is the value of f(5)

    My working:

    2f(4) = 2(f(2))^2 = 2((f(1)^2))^2

    I can't figure out what to do next.
    Keep going. You've expressed f(5) in terms of f(4), f(4) in terms of f(2), f(2) in terms of f(1)... What does the definition of f say you should do with f(1)?
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    (Original post by UCASLord)
    The next logical step I can think of for this question is 2((f(1)^2))^2 = 2(((f(0.5)^2)^2)^2)
    Hang on a moment - is 1 even or odd?!
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    (Original post by UCASLord)
    Sorry for taking a while to get back to you, I was working on other problems and only looked at my computer now :P

    The next logical step I can think of for this question is 2((f(1)^2))^2 = 2(((f(0.5)^2)^2)^2)

    The issue is that I can just keep going like this, with that number approaching infinity, but never reaching it so I would never actually get to a situation where n = 0. Of course, it does say "for any integer" in the question, but it doesn't specify what to do with non-integers.
    If it says "for any integer" then it's telling you that you can only apply the rules when n is an integer - this should be a pointer to the fact that you've gone wrong somewhere

    Also note that you have a typo in your original post - you should have n >= 0, not n <= 0.
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    (Original post by UCASLord)
    ... Wow.

    :facepalm2:

    Thanks for you help :P
    These things happen when you're in the middle of a load of MAT problems...
 
 
 
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