The original poster is exploring the limit as n approaches infinity for the expression (1 + 1/n)^n, recognizing it as the mathematical constant "e." They seek to transform this limit into a series to facilitate a proof, specifically comparing it to the infinite series sum from n=0 to infinity for 1/n!.
The discussion is ongoing, with participants sharing insights about series expansions and Taylor series. There is no explicit consensus yet, but the conversation is moving towards understanding how to relate the limit to a series representation.
There may be constraints related to the original poster's understanding of series and limits, as well as the need to adhere to homework guidelines that discourage direct solutions.
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! + ...possum said:not in full, but f(0)*(X-x0)+f(1)*(x-x0)/1!+f(2)*(x-x0)/2!...? yes?