Question 1
Let $(x_n)$ be defined by $x_1=2$ and $x_{n+1}=\sqrt{x_n+8}-\sqrt{x_n+3}$ for $n\ge1$.
(a) Prove that $(x_n)$ has a finite limit and find it.
(b) Prove that $n\le x_1+x_2+\cdots+x_n\le n+1$ for every positive integer $n$.
(a) Prove that $(x_n)$ has a finite limit and find it.
(b) Prove that $n\le x_1+x_2+\cdots+x_n\le n+1$ for every positive integer $n$.