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December 18th, 2018, 06:50 AM  #1 
Member Joined: Nov 2012 Posts: 80 Thanks: 1  Mathematic induction
In the suggested answer on the second page, it says 1<=(2n+1)/2n. However, I doubt that the fraction should be only greater than 1 instead of being equal and greater than 1 for n = 1,2,3,.... Could anyone tell me why the inequality include the equal sign?

December 18th, 2018, 07:33 AM  #2 
Senior Member Joined: Dec 2015 From: Earth Posts: 819 Thanks: 113 Math Focus: Elementary Math 
For n=1,2,3... it could be written as < But $\displaystyle \leq $ makes sense too , it means = or < Example $\displaystyle 2 \leq 2$ is true Sometimes it holds true for both , $\displaystyle 1\leq n$ Last edited by idontknow; December 18th, 2018 at 07:37 AM. 
December 18th, 2018, 05:57 PM  #3 
Member Joined: Nov 2012 Posts: 80 Thanks: 1 
Oh, I see. => literally means = or >. Either case can fulfill the requirment. Thank you for your helpí ¾í´—


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