Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
AP

Posts: 137
Registered: 3/4/09
on real part of [(1+isqrt(7))/2]^n
Posted: Feb 10, 2014 12:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Be a=(1+isqrt(7))/2 and a_n=the real part of a^n

question : show lim |a_n | is +inf ? (it-is not a home-work..)

first values of 2a_n , n>=0, : 2/1/-3/-5/1/11/9/-13/-31/-5/57/

we have
(1-2z)/(2-z+z^2)=sum_{n>=0 } (a_{n+1}/2^n)z^n for |z|<sqrt(2)
=1/2-(3/4)z-(5/8)z^2+(1/16)z^3+...

(if b=(1-isqrt(7))/2, 1/(a-z)+1/(b-z)=...)

the radius of convergence is R>=sqrt(2)
but if R>sqrt(2) we obtain a contradiction because (1-2z)/(2-z+z^2) is
not define for a (|a|=sqrt(2))
so R=sqrt(2)

hence, if z=2 , the series diverges and |a_n| is not bounded.
But , after ...




---
Ce courrier électronique ne contient aucun virus ou logiciel malveillant parce que la protection avast! Antivirus est active.
http://www.avast.com




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.