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Topic: on real part of [(1+isqrt(7))/2]^n
Replies: 20   Last Post: Feb 15, 2014 5:52 AM

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William Elliot

Posts: 1,705
Registered: 1/8/12
Re: on real part of [(1+isqrt(7))/2]^n
Posted: Feb 11, 2014 11:41 PM
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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.



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