If a 1 , a 2 , a 3 , . . ., a n are in A.P. where a i > 0 then 1 a_ 1 + a_ 2 + 1 a_ 2 +…
Mathematics · JEE Advanced · NTA Exams — Progression and Series
If a1, a2, a3, . . ., an are in A.P. where ai > 0 
then
\(\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}=\)
then \(\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}=\)
- \(\frac{\mathrm{n}-1}{\sqrt{\mathrm{a}_{1}}+\sqrt{\mathrm{a}_{\mathrm{n}}}}\)
- \(\frac{\mathrm{n}+1}{\sqrt{\mathrm{a}_{1}}+\sqrt{\mathrm{a}_{\mathrm{n}}}}\)
- \(\frac{\mathrm{n}-1}{\sqrt{\mathrm{a}_{1}}-\sqrt{\mathrm{a}_{\mathrm{n}}}}\)
- \(\frac{\mathrm{n}+1}{\sqrt{\mathrm{a}_{1}}-\sqrt{\mathrm{a}_{\mathrm{n}}}}\)
Answer
(A) n -1 a _ 1 + a _ n
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