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Can someone please show me how to do these. i keep getting the wrong answer
T(n+1) = 3 x Tn x 2^n
a) By substituting n=2 into the rule determine T3... should equal 36
b) By substituting n=3 into the rule determine T4... should equal 864
I don't understand your question. Are you trying to find the base value of T, like T(1)? Or are you trying to find a non-recursive definition of T(n)?
If it's the first, the problem is easy. You know T(3) = 3 x T(2) x 2^2 = 3 x 4 x T(2) = 36, so T(2) = 3. Using this same method you can find that T(1) = 1/2.
If you need a non-recursive definition of T(n), try looking backwards. What I mean is to do something like this:
The pattern here is pretty easy to see. We have 3 raised to the power of n-1 at the start. We then have 2 raised to the power of n^2 - (sum from i = 1 to n of i). This is then multiplied by our base T(1), which we know from above is 1/2. This leaves us with
Let's check that this is right. For T(1) we get 3^0 x 2^(-1) = 1/2. For T(2) we get 3^1 x 2^0 = 3. For T(3) we get 3^2 x 2^2 = 36. And finally, T(4) = 3^3 x 2^5 = 864, all of which are what we expected.
Wrap it in bacon
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another way of doing it
Last edited by Dragonshade (2008-05-08 03:22:53)
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