Homework Help: From limit to an infinate series.

1. Sep 23, 2005

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

2. Sep 24, 2005

Tom Mattson

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

3. Sep 26, 2005

possum

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

4. Sep 26, 2005

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.