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December 18th, 2018, 06:50 AM   #1
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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?
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December 18th, 2018, 07:33 AM   #2
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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 , $\displaystyle 1\leq n$
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Last edited by idontknow; December 18th, 2018 at 07:37 AM.
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December 18th, 2018, 05:57 PM   #3
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Oh, I see. => literally means = or >. Either case can fulfill the requirment. Thank you for your help🤗
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