I am struggling to write a formal proof for the following problem. I know that you can multiply by the conjugate and the get the sum of the two square roots over the quantity one. Then $\displaystyle sqrt(n + 1)$ goes to infinity and $\displaystyle sqrt(n)$ also goes to infinity, thus the sum goes to infinity. If the whole denominator goes to infinity, then one over the denominator goes to zero.

However, I don't know if that is a sufficient proof. I would appreciate any further insight anyone can offer. Thank you in advance.

Problem:

Show that $\displaystyle lim| sqrt(n + 1) - sqrt(n) | = 0$.