Recent questions tagged limits

Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$

$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.