If a1,a2,a3,…,an are in arithmetic progression, where a1>0 for all i – InterviewSolution

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1.	If a1,a2,a3,…,an are in arithmetic progression, where a1>0 for all i. Prove that 1√a1+√a2+1√a2+√a3+…+1√an−1+√an=n−1√a1+√an
Answer» If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ are in arithmetic progression, where $a_{1} > 0$ for all i. Prove that $\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \dots + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{n - 1}{\sqrt{a_{1}} + \sqrt{a_{n}}}$

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