I have been given that a1 = 1 and an+1 = 1/3*(an + 4). In order to prove that this sequence is monotonous, what is the second step of mathematical induction? If my explaining of the question is unclear, here is a picture of the question and the possible answers. I believe the answer is C but I welcome any correction/confirmation.
gyazo . com/85e9ff97c6139e1d0ccb1054f1c30e5e.png
3 answers
Monotonic*
you need to show that
a<n+1> > a<n> (increasing)
or
a<n+1> < a<n> (decreasing)
If you expand the expression from the recursion, you can clearly see that it is.
Once you can show that each term is greater (or less) than the previous one, then you have shown that the entire sequence is monotonic (and thus, monotonous!).
a<n+1> > a<n> (increasing)
or
a<n+1> < a<n> (decreasing)
If you expand the expression from the recursion, you can clearly see that it is.
Once you can show that each term is greater (or less) than the previous one, then you have shown that the entire sequence is monotonic (and thus, monotonous!).
Thank you Steve for the response. So from what you have said, I first assume that a<n+1> > a<n> and then prove that the corresponding expression is true? Or is it the other way around?
3 answers