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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:

ht tp://i46.tiny pic(.)(com)/qz0oat . jpg
(remove parentheses and spaces)
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. Help is VERY appreciated.

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