Home
Class 12
MATHS
If S be the sum, P the product and R the...

If S be the sum, P the product and R the sum of the reciprocal of n terms in G.P., prove that, `p^(2) = ((S)/(R ))^(n)`.

Answer

Step by step text solution for If S be the sum, P the product and R the sum of the reciprocal of n terms in G.P., prove that, p^(2) = ((S)/(R ))^(n). by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 D (Multiple Choice Type Questions)|2 Videos
  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 D (Very Short Answer Type Questions)|27 Videos
  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Short Answer Type Questions)|43 Videos
  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos
  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If S be the sum. P be the product,and R the sum of the reciprocals of n terms in a G.P., Prove that P^2=(S/R)^n

Let S be the sum, P the product, and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n=S^ndot

If a be the first term, l the nth and p the product of first n terms of a G.P. show that, p^(2) = (al)^(n) .

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .

If S_1,S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=((S_2)-(S_1))^2

The nth term of an A.P. is p and the sum of its first n terms is q. Prove that its first term is (1)/(n)(2q-p n) .

If the first and the n^("th") term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

If s_1 be the sum of (2n+1) terms of an A.P and s_2 be the sum its odd terms, then prove that s_1:s_2=(2n+1):(n+1)

If the sum of the first m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, prove that, (m+n)((1)/(m)-(1)/(p)) = (m+p)((1)/(m) - (1)/(n))

If the first and the nth terms of a G.P are a and b , respectively, and if P is the product of the first n terms then prove that P^2=(a b)^ndot