1. Sep 23, 2005 #1

   possum

   

   I am looking for a method to express limit n goes to infinity for the quantity (1+1/n)^n .....I know and recognisee this as "e" , but i need to transform it into a series to prove it. I plan to compare the transformed limit expression to "sum from n=0 to n=infinity for 1/n! how can I re express this?
   
   POSSUM

    

   possum, Sep 23, 2005
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3. Sep 24, 2005 #2

   Tom Mattson

   

   Staff Emeritus

   Science Advisor

   Gold Member

   Do you know how to find a power series for a function?

    

   Tom Mattson, Sep 24, 2005
4. Sep 26, 2005 #3

   possum

   

   not in full, but f(0)*(X-x0)+f(1)*(x-x0)/1!+f(2)*(x-x0)/2!.........? yes?

    

   possum, Sep 26, 2005
5. Sep 26, 2005 #4

   hypermorphism

   

   The 1-dimensional Taylor series of a function centered at a point x₀ in the domain is f⁽⁰⁾(x₀)*(x-x₀)/0! + f⁽¹⁾(x₀)*(x-x₀)/1! + f⁽²⁾(x₀)*(x-x₀)/2! + ...
   where f⁽ⁱ⁾(x₀) is the ith derivative of f at x₀. See Taylor series for more detailed analysis.

    

   hypermorphism, Sep 26, 2005

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