Q. 6

# Mark the correct alternative in each of the following:

If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then is equal to

A. S/R

B. R/S

C.

D.

Answer :

Let the GP is a , ar , ar^{2} , ar^{3} , .......... arⁿ⁻^{1}.

S = Sum of n terms

= a + ar + ar^{2} + ar^{3} + .......+ arⁿ⁻^{1}

and R = sum of reciprocal of n terms

P = product of n terms = a × ar × ar^{2} × ar^{3} × .....× arⁿ⁻^{1}

=(a^{1}⁺^{1}⁺^{1}⁺^{1}⁺^{1}⁺^{1}⁺^{1}⁺⁻⁻^{1})(r^{1}⁺^{2}⁺^{3}⁺⁻⁻⁻⁻⁽ⁿ⁻^{1}⁾〉

take square both sides,

⇒

⇒

⇒

Thus,

⇒

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(i)

(ii)

(iii)

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