Question about discrete math.
I don't know i should be posting here, but this homework problem is in CMPSC 313 so it may seem computer guys should be able to do that because it's in a computer science course.
Anyways, sooo recently i've been studying the method of induction. and we are working on proving mathematical statement using that method. However, i got stuck when i got this..
Show that X(n+2) = 10/3 * (X(n+1)) - X(n) is Xn = (1/3) ^ n for X0 = 1 X1 = 1/3
so i start by the base case so
when n = 0
x2 = 10/3 * X1 - X0 <========> x2 = (1/3)^2
=> 1/9 <<====>> 1/9
so yea i got the base case down but i don't know how to move further anyone can help?
Anyways, sooo recently i've been studying the method of induction. and we are working on proving mathematical statement using that method. However, i got stuck when i got this..
Show that X(n+2) = 10/3 * (X(n+1)) - X(n) is Xn = (1/3) ^ n for X0 = 1 X1 = 1/3
so i start by the base case so
when n = 0
x2 = 10/3 * X1 - X0 <========> x2 = (1/3)^2
=> 1/9 <<====>> 1/9
so yea i got the base case down but i don't know how to move further anyone can help?
yea i did that, that's where i got stuck.
(1/3) ^ (n +2) = 10/3 * (X(n+1)) - X(n). here's where i got stuck, i dont' know how to deal with those x(n) and X(n+1). when i was doing other simpler practice problems there isn't anything like that.
(1/3) ^ (n +2) = 10/3 * (X(n+1)) - X(n). here's where i got stuck, i dont' know how to deal with those x(n) and X(n+1). when i was doing other simpler practice problems there isn't anything like that.
The formula you posted is wrong. 10/(3 * X1) - X0 is 9, not 1/9. If I mess around with the brackets, I get division by zero.
That said, your next step is to "evaluate" Xk and Xk+1 using the formula Xn = (1/3)n. The goal here is not to get an answer, just two formulae for Xk = ... and Xk+1 = ...
Next, you need to "evaluate" Xk+2 using the formula Xn = (1/3)n. If all goes well, after some simplification you should be able to extract the original identity, Xn+2 = 10/3 * (Xn+1) - Xn (or whatever it is) with k substituted for n
EDIT: Actually when you "evaluate" Xk+2 you should use the formula Xn+2 = .... You then need to plug in Xk and Xk+1 whose formulae you derived earlier. You should be able to simplify it to Xk+2 = (1/3)k+2
That said, your next step is to "evaluate" Xk and Xk+1 using the formula Xn = (1/3)n. The goal here is not to get an answer, just two formulae for Xk = ... and Xk+1 = ...
EDIT: Actually when you "evaluate" Xk+2 you should use the formula Xn+2 = .... You then need to plug in Xk and Xk+1 whose formulae you derived earlier. You should be able to simplify it to Xk+2 = (1/3)k+2
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@hunkeelin:
Read my previous post carefully. You don't do what I suggest.
You assume that xn+2 = (1/3)n+2. That's what you must prove.
Read my previous post carefully. You don't do what I suggest.
You assume that xn+2 = (1/3)n+2. That's what you must prove.
Last edited on
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