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If a1,a2,a3, ,an are in A.P., where ai >...

If `a_1,a_2,a_3, ,a_n` are in A.P., where `a_i >0` for all `i` , show that `1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot`

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To prove the given statement, we will follow these steps: ### Step 1: Understand the properties of A.P. Given that \( a_1, a_2, a_3, \ldots, a_n \) are in Arithmetic Progression (A.P.), we can express the terms as: \[ a_2 = a_1 + d, \quad a_3 = a_1 + 2d, \quad \ldots, \quad a_n = a_1 + (n-1)d \] where \( d \) is the common difference. ...
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