Subject: discrete mathematics
the level of the question  college Hi! I'm having a lot of trouble with this question. A sequence c is defined recursively as follows:
c0 = 2 ck= 5ck3 for all integers Prove that cn is even for all integers.
This is what I have done so far: This is where I am stuck...I'm not sure.. I might actually be going about this problem completely wrong since it says that you need to prove cn is even. Can you help me? =/ Thank you very much!! Hi,
We think that you may be reading the question incorrectly. You are to show that c_{n} is even for all integers where
You are probably best to use "Strong Induction" for this sequence. In this case, your induction hypothesis should read: "assume c_{k} is even for all natural numbers k such that 0< = k < n" Your final step is to show that c_{n} is even using the definition of the sequence, i.e. If n >= 3, c_{n} = 5c_{n3} will be even because c_{n3} will be even by our induction hypothesis. Your basic step took care of the case where n = 0, 1 and 2 and we have successfully proved the result is true for all n >= 3. Hope this helps,Leeanne and Penny
