Question 22
The arithmetic sequence $(a_n)$ has first term $a_1=1$ and common difference $d=8$. Evaluate
$$S=\frac1{\sqrt{a_1}+\sqrt{a_2}}+\frac1{\sqrt{a_2}+\sqrt{a_3}}+\frac1{\sqrt{a_3}+\sqrt{a_4}}+\cdots+\frac1{\sqrt{a_{253}}+\sqrt{a_{254}}}.$$
$$S=\frac1{\sqrt{a_1}+\sqrt{a_2}}+\frac1{\sqrt{a_2}+\sqrt{a_3}}+\frac1{\sqrt{a_3}+\sqrt{a_4}}+\cdots+\frac1{\sqrt{a_{253}}+\sqrt{a_{254}}}.$$