Can Anyone Prove why e^x= (1+x/n)^n as n approaches Infinity

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    E^x Infinity
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SUMMARY

The discussion centers on proving the mathematical identity e^x = (1 + x/n)^n as n approaches infinity. Participants emphasize the importance of understanding the definition of e^x, particularly in the context of limits and substitutions. The substitution m = n/x is suggested as a starting point for the proof. Clarity on the definition of e^x is crucial for progressing in the proof.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with the definition of the exponential function e^x
  • Knowledge of substitution techniques in mathematical proofs
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the formal definition of e^x and its derivation
  • Learn about limits and their properties in calculus
  • Explore substitution methods in mathematical proofs
  • Investigate the concept of convergence in sequences and series
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Students of calculus, mathematicians, and anyone interested in understanding the foundations of exponential functions and their proofs.

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Can anyone help me ? I am completely lost on this one
 
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tam421602 said:
Can anyone help me ? I am completely lost on this one

Hello,
Start by using the substitution:

m=\frac{n}{x}

What did you get?
 
First you will need a definition of e^x ... what is yours?
 

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