Simple Limit - Calculus

What a boring question.

$$ There's a bit of typo in the question. It should be $\lim\limits_{N \to \infty} \sum\limits_{k=0}^N \left(\frac{1}{2}\right)^k$ . It can easily be solved because the series forms a geometric progression. The solution is $\lim\limits_{N \to \infty} \sum\limits_{k=0}^N \left(\frac{1}{2}\right)^k = 1 + \frac{1}{2} + \frac{1}{4} + \cdots = \frac{1}{1-\frac{1}{2}} = \boxed{2}.$ $$ $\text{\# }\mathbb{Q}.\mathbb{E}.\mathbb{D}.\text{\#}$

First let's just take a look at what's going on here. Plugging in zero, we get 1. From there on out, it's just the harmonic series, which we know sums up to 1. And the most tricky part: 1 + 1 = 2.