quasi
Posts:
12,021
Registered:
7/15/05


Re: on real part of [(1+isqrt(7))/2]^n
Posted:
Feb 15, 2014 4:29 AM


>konyberg > >a_n = (sqrt(2))^n * cos(n*acos(sqrt(2)/4)) > > = (sqrt(2))^n * cos(n*acos(sqrt(2)/4)) > >where cos(n*acos(sqrt(2)/4)) can be considered as a "constant" >different from 0.
Certainly not!
Different from 0 doesn't mean it can be considered as a "constant".
For example, how do you know that there aren't infinitely positive integers n such that
cos(n*acos(sqrt(2)/4)) < 1/sqrt(2)^n
??
You don't.
>Conclusion: The limit a_n goes to infinity as n goes to >infinity.
No, it's not even close to a proof.
quasi

