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= 5ck-3 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 cn 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 ck is even for all natural numbers k such that 0< = k < n"
Your final step is to show that cn is even using the definition of the sequence, i.e.
If n >= 3, cn = 5cn-3 will be even because cn-3 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