Is it true that $\lim_{n\to \infty}\sum_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n} = 0$?

Question

This problem originates from taking the limit of a Riemann Sum to evaluate an integral. In short, to help solve the limit, I used the bound $$\sum_{i=1}^{n}\frac{1}{\sqrt{i}} \leq 2\sqrt{n}$$ Which intuitively seemed to work just by looking at the graph of these functions. Nonetheless, after substituting $2\sqrt{n}$ for the sum in the limit in question, I got my desired result! This led me to ask the question, is it true that $$\lim_{n\to \infty}\sum_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n} = 0$$ I personally do not know how to even begin to solve this limit since clearly both of them diverge (the sum is greater than the Harmonic Series).