If ${a_1},\;{a_2},\;{a_3}.......{a_n}$ are in $A.P.$, where ${a_i} > 0$ for all $i$, then the value of $\frac{1}{{\sqrt {{a_1}} + \sqrt {{a_2}} }} + \frac{1}{{\sqrt {{a_2}} + \sqrt {{a_3}} }} + $ $........ + \frac{1}{{\sqrt {{a_{n - 1}}} + \sqrt {{a_n}} }} = $
If ${a_1},\;{a_2},\;{a_3}.......{a_n}$ are in $A.P.$, where ${a_i} > 0$ for all $i$, then the value of $\frac{1}{{\sqrt {{a_1}} + \sqrt {{a_2}} }} + \frac{1}{{\sqrt {{a_2}} + \sqrt {{a_3}} }} + $ $........ + \frac{1}{{\sqrt {{a_{n - 1}}} + \sqrt {{a_n}} }} = $
- [IIT 1982]
- A
$\frac{{n - 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}$
- B
$\frac{{n + 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}$
- C
$\frac{{n - 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}$
- D
$\frac{{n + 1}}{{\sqrt {{a_1}} - \sqrt {{a_n}} }}$
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