Deriving the series of e using binomial theorem
I need help understanding how the series of e derives into the exponential series using the binomial theorem.
Here is a link to a pic of a page in my book, regarding the exponential series:
A couple of questions:
Where does the [1 + (1/k)]^k come from and why is it used?
Could you clarify the expansion of [1+(1/k)]^k?
I don't understand how it gets to ... k(1/k) + k(k-1)/2! (1/k^2) + ...
How does it end up with a 1 + 1 + 1[1-(1/k)]/2! + ...
Why are you finding the limit of the series?
And finally how do you end up with exponential series
x^n /n! = 1 + x + x^2/2! + ... ?
I'm confused and just really don't understand why or how you end up with everything. Try and keep it simple, please. Help is VERY appreciated.