Representing e^x As An Infinite Series

Before starting the proof, you have to be familiar with the binomial theorem:

Let a = 1 and b = c/n:

Now lets focus on the blue part of the above equation:

Now lets simplify further:

Look at the red part, there are i terms in total:

So basically:

Now let n -> ∞:

Lets simplify:

We can substitute the limit on the left hand side with ec:

To understand why the limit is equal to ec, read this.

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