
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 25th, 2013, 03:08 AM  #1 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Algebra trick to make this induction proof work?
Hello there, For two days, I have tried to prove that this is true using induction: is true. I checked. The best I could ever arrive at, assuming to be true, was: . However, I suspect there is a prettier solution, and I am unable to continue my happy life without knowing what it was. Are any of you able to work it out? Thank you for your time. Kind regards, Marius 
August 25th, 2013, 05:45 AM  #2 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Re: Algebra trick to make this induction proof work?
I found the solution myself: Thank you for your time. Kind regards, Marius 
August 25th, 2013, 05:52 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,379 Thanks: 2011 
Your work is okay. Obviously, ?(k+2)/?(k+1) + 1 > 2. Multiplying by ?(k+2)/?(k+1)  1 gives 1/(k+1) > 2(?k+2)/?(k+1)  1), which implies 1 > 2(?(k+2)?k+1))  2(k + 1), as needed to complete the induction proof. 
August 25th, 2013, 05:56 AM  #4 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Re: Algebra trick to make this induction proof work?
Thanks skipjack, what do you think of my other attempt? Thanks.M 
August 25th, 2013, 07:08 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,379 Thanks: 2011 
Both are okay. The first is abbreviated and unfinished, whilst the second fills out the first and finishes it.


Tags 
algebra, induction, make, proof, trick, work 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
proof by induction  fe phi fo  Calculus  4  June 12th, 2012 08:47 AM 
Disproving convergence: does my proof make sense?  DenJansen  Real Analysis  1  February 20th, 2012 09:33 PM 
Need to make sure I am starting a proof right  restin84  Applied Math  3  October 10th, 2009 07:22 AM 
Algebra work problem  mikeportnoy  Algebra  3  February 18th, 2009 11:51 AM 
proof by induction  MaD_GirL  Number Theory  5  November 14th, 2007 06:34 PM 