1.

हक पक की दद दर न. - = MoyL&कला शी aiकण. भूकर 9, A, Og 4८ R aae AT an दि सा o Lou शव

Answer»

a₁, a₂, a₃ , ......... an are in AP. so, a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = ...... = an₋₁ - an = d also, a₂ = a₁ + d, a₃ = a₂ + d , a₄ = a₃ + d ...... , an = an₋₁ + (n-1)d

Now, LHS = 1/a₁.a₂ + 1/a₂a₃ + 1/a₃a₄ + ..... + 1/an₋₁.an = 1/a₁(a₁ + d) + 1/a₂(a₂ + d) + 1/a₃(a₃ + d) + ....... 1/an₋₁(an₋₁ + d) = 1/d[ 1/a₁ - 1/(a₁ + d) + 1/a₂ - 1/(a₂ + d) + 1/a₃ - 1/(a₃ + d) + ....... +1/an₋₁ - 1/an ]= 1/d [1/a₁ - 1/a₂ + 1/a₂ - 1/a₃ + 1/a₃ - 1/a₄ + ......... + 1/an₋₁ - 1/an ]= 1/d[ 1/a₁ - 1/an ]= 1/d(an - a₁)/a₁.an

We know, an = a₁ + (n-1)d an - a₁ = (n-1)d

= 1/d × (n-1)d/a₁an = (n-1)/a₁an = RHS

Hence proved



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