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Question

If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, than P2 is equal to


A

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B

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C

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D

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Solution

The correct option is D


Given that sum S = a(rπ1)r1 = a(1rπ)(1r) ..........(i)

P = a(ar)(a r2) ..........(a rπ1) = aπ r1+2++(π1)

= aπ r(π1)π2 i.e., P2 = a2π rπ(π1) ...........(ii)

and R = 1a + 1ar + 1ar2 + .........upto n terms

= 1a ( 1 + 1r + 1r2 + ...........upto n terms)

= 1a[1rn1](1r1) ( ∵ 1r > 1) if r < 1

= (1rπ)arπ1(1r) --------(iii)

Therefore, SR = a(1rπ)1r × arπ1(1r)(1rπ) = a2 a2π1

or (SR)π = a2rπ1π = a2π rπ(π1) = P2.


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