Geez, can you please stop being so defensive. I'm sorry for reading your post, if you don't want me to read the working and make absolutely no comments about it then delete that part of the post.
Nah, not being defensive, just again wondering if you can read. I did post what the actual matrix equation should be with 3x3, but of course you chose to conveniently not see it
And never occurred to you that I left my incorrect working because I intended to go back and change it which is why I put it in a spoiler? Or that I left it to show the process even if the matrices are incorrect, so if anyone chose to do it they could, using the correct 3x3?
As for the double induction - Yes that is why I said "simple induction" won't work, but of course I would like to see if there is some stronger induction that could be done.
Because it shows that straightforward induction won't work (but of course as you mentioned a stronger one may). Please read my other post for an explanation.
Now, I never said "simple induction" did I? You just assumed that because it was someone else's idea ( I have yet to see your method of approaching this problem, nor anything really constructive either), that it would be "simple"? I meant, if I so wanted to, I could use 2 assumption P(k-1) and P(k) times them or raise each to a power then substitute into P(k+1). I haven't tried this yet, redoing the matrices atm so don't leap to the opportunity of being able to attack someone again
When I said induction in the first place, I meant
any sort of induction, if I wanted to I could prove that
is irrational using induction, and I'd still call that a proof by induction.
Although, perhaps I'm being a bit harsh on you! after all, your worth while contribution:
Let P(n) be the statement: and
Then Is clearly true since it just says and . Then assuming P(n), you may derive P(n+1) with some straightforward algebra.
I'm still wondering how you guessed the correctly.
You mind actually helping FlorianK then? Afterall, its just some "straightforward algebra". And you're such a nice person, labelling it a "guess". I'm sure your opposed to penicillin too, since that was an accident. Btw, if you were actually curious, you can run the numbers too and come to a similar conclusion.