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1 Answer
- 6 years ago
For a start, put x=2 to get f(2) = f(1) - f(0), f(0) =2.
Do the series: f(x) = f(x-1) - f(x-2) = f(x-2) - f(x-3) - f(x-2) = - f(x-3) since f(x-1) = f((x-1) - 1) - f((x-1) - 2) and so on. If you go on with the series you'll get f(x) = f(x-6) and so on... f(x) = -f(x-9)... we now see that f(x) will always equal an f(x) = f(x-n) where n is a multiply of 3. For even multiplies it is f(x) = f(x-n) but for odd ones it's f(x) = - f(x-n). Since 2013 is an odd multiply, f(x) = -f(x-2013) = -f((x-2013) - 1) + f((x-2013) - 2) = -f(x-2014) + f(x-2015). Always be careful with the signs + and -. For x= 2015, f(2015) = -f(1) + f(0) = -3 + 2 = -1
Source(s): Hard math :)
