Irrational number e

 

 

 

 

 

 

 

 

 

 

 

 

Consider the binominal expansion of (1 + )n where n is a positive interger.

When n tends to infinity,

tend to zero.  Also,  n! =

The coefficient of the general term(the (r+1)th term) is :

We take

    

When x = 1, we have

    

  or 

    where

 

Discovery of Natural Logarithms 自然對數的發現

Consider a function

  

  

  If we change the base of the logarithm from a to e, we have = 1.

  The logarithm with base e is called Natural Logarithm.

  Therefore, when  

     

  Hence,   + C

      or   where C' is a constant