From limit to an infinate series.

[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

 

[Tom Mattson]

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

 

[possum]

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

 

[hypermorphism]

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

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.