Solving with mathematical induction

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Homework Help Overview

The problem involves proving an inequality using mathematical induction, specifically the expression 1/2n <= (2n - 1)!/(2n!). Participants are exploring the steps necessary to establish the validity of this inequality for all natural numbers n.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks hints on how to approach the problem. Some participants suggest starting with a base case for n = 1 and then moving to the inductive step. Others question the understanding of proof by induction and the equivalence of expressions for different values of n.

Discussion Status

The discussion is ongoing, with participants providing initial steps and questioning the nature of mathematical induction. There is no explicit consensus on the approach, but some guidance on proving the base case and the inductive step has been offered.

Contextual Notes

Participants are discussing the requirements of mathematical induction and the specific expressions involved in the proof, indicating a need for clarity on definitions and steps in the process.

gr3g1
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I have to solve:

1/2n <= (2n - 1)!/(2n!)

I have no idea how to approach this problem..

Any hints?
Thanks
 
Last edited:
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prove that it is true when n = 1. then you should show that 1/2(n+1) <= [2(n+1)! - 1)]/[2(n+1)!]
 
Where would I go from here?
 
What IS "proof by Induction"? Surely you didn't just walk into the wrong class!
 
I think I have to prove the RHS of the equation
is equivalent for P(k) and P(k+1)
is that right?
 
More precisely:

(2k - 1)! / (2k)! == (2(k+1)-1)! / (2(k+1)!)
 
Last edited:

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