
Re: on real part of [(1+isqrt(7))/2]^n
Posted:
Feb 11, 2014 11:41 PM


On Wed, 12 Feb 2014, Robin Chapman wrote: > On 12/02/2014 04:25, William Elliot wrote:
> > > Let a=(1+isqrt(7))/2 and a_n=the real part of a^n > > > question : show lim a_n  is +inf ? > > > > That's not a question. That's an exercise. > > > > Let r = sqr 7, b = 1 + ir. > > > > Below I show how to prove the limit is infinite for 1 + i.sqr 7. > > Really? > > > d_n = sum(j=1,[n/2]) n_C_2j (7)^j < re(b^n) > > (d_n)^2 = sum(j,k=1,[n/2]) n_C_2j n_C_2k 7^(j+k) > oo as n>oo. > > What happened to all those minus signs?
Shucks, still there if j is odd and k even.

