Solving Algebraic Equations: Need Help?

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SUMMARY

The discussion focuses on solving algebraic equations involving factorials and approximations. A user expresses difficulty in starting the problem, specifically mentioning attempts to apply logarithmic properties and Stirling's approximation without success. The solution proposed involves expanding the factorial expression using the highest powers of N/2, leading to a simplified form that includes terms of (N/2)^m and (N/2)^(m-1). This method provides a structured approach to tackle the algebraic equation effectively.

PREREQUISITES
  • Understanding of algebraic equations and factorial notation
  • Familiarity with Stirling's approximation
  • Basic knowledge of logarithmic functions
  • Ability to manipulate polynomial expressions
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  • Study the application of Stirling's approximation in combinatorial problems
  • Learn about polynomial expansion techniques
  • Explore logarithmic properties in solving equations
  • Investigate advanced factorial identities and their applications
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Students studying algebra, mathematicians, and anyone seeking to improve their problem-solving skills in algebraic equations involving factorials and approximations.

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Homework Statement




Please see attached

Homework Equations





The Attempt at a Solution



Not sure how to begin actually...

I've tried taking logs of both sides and using sterling's approximation but it came to nothing... :(

Any ideas? Thanksss
 

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any ideas anyone?
 
They are using things like (N/2+m)!/(N/2)!=(N/2+m)*(N/2+(m-1))*...*(N/2+1). Expand the right side keeping only the two highest powers of N/2. You get (N/2)^m+(m+(m-1)+...+2+1)*(N/2)^(m-1).
 

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