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





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