SEAMO 2027 - Paper E - SET 01 - Self-study Question 9

Let $u_1,u_2,\ldots,u_{49}$ be an increasing arithmetic progression with first term $25$ and common difference $3$. Find $\frac3{\sqrt{u_1}+\sqrt{u_2}}+\frac3{\sqrt{u_2}+\sqrt{u_3}}+\cdots+\frac3{\sqrt{u_{48}}+\sqrt{u_{49}}}$.