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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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 Robin Chapman Posts: 412 Registered: 5/29/08
Re: on real part of [(1+isqrt(7))/2]^n
Posted: Feb 11, 2014 11:35 PM

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?

Date Subject Author
2/10/14 AP
2/10/14 Brian Q. Hutchings
2/10/14 Pubkeybreaker
2/10/14 Karl-Olav Nyberg
2/10/14 William Elliot
2/11/14 AP
2/11/14 Karl-Olav Nyberg
2/11/14 Robin Chapman
2/11/14 Karl-Olav Nyberg
2/11/14 Robin Chapman
2/11/14 Karl-Olav Nyberg
2/11/14 Karl-Olav Nyberg
2/15/14 Karl-Olav Nyberg
2/15/14 quasi
2/15/14 Karl-Olav Nyberg
2/15/14 quasi
2/11/14 William Elliot
2/11/14 Robin Chapman
2/11/14 William Elliot
2/13/14 quasi
2/14/14 Brian Q. Hutchings