Find the sum of the sequence? I have the following sequence:

I need to find the sum of it. However I know that the sequence is not geometrical or arithmetic, therefore I don't know which formula would I use to find the sum.
I wrote a general sum equation: 
and I'm trying to tackle the problem this way but
this problem does not involve higher mathematics, therefore I know that there is a much more easier solution to it.
As you can see wolfram alpha app for series gave me the correct answer, but I would need the steps if possible.

$$ \forall n \in \mathbb{N}, \qquad \sum_{k=1}^n \dbinom{n}{k} 2^{n-k} (-1)^k = \left(2 - 1\right)^n = (-1)^n.$$
Put $n = 100$ and you're done.
