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)`.

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

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)

If S be the sum, P the product and R the sum of the reciprocal of n te...
Text Solution
|
If S(1), S(2), S(3) be respectively the sums of n, 2n and 3n terms of ...
Text Solution
|
If the sum of first n terms of G.P. is S and the sum of its first 2n t...
Text Solution
|
If S(n) = 1 + (1)/(2) + (1)/(2^(2))+….+(1)/(2^(n-1)), find the least v...
Text Solution
|
If u(1), u(2), u(3),… form a G.P. with common ratio k, find the sum of...
Text Solution
|
Find the sum to n terms of the following series: (x+1/x)^2+(x^2+1/(x^2...
Text Solution
|
If the first term, common ratio and the sum of first n terms of a G.P....
Text Solution
|
When a certain golf-ball is dropped on a piece of pavement, it bounces...
Text Solution
|
If the A.M. of two numbers be twice their G.M., prove that two numbers...
Text Solution
|
If A and G be the A.M. and G.M. of two numbers , show that the numbers...
Text Solution
|
If a, b, c form an A.P. and b, c, a form a G.P., show that (1)/(c ), (...
Text Solution
|
If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y)...
Text Solution
|
The sum of three numbers in A.P. is 15. If 1, 4 and 19 are added to th...
Text Solution
|
The sum of three numbers in A.P. is 18. If 2, 2, 6 are added respectiv...
Text Solution
|
Three terms are in G.P. Their product is 216. If 4 be added to the fir...
Text Solution
|
Find the sum to n terms of each of the following series : 1 + 11 + 1...
Text Solution
|
Find the sum to n terms of each of the following series : 2 + 22 + ...
Text Solution
|
0.8 + 0.88 + 0.888 + …
Text Solution
|
Find the sum to n terms of each of the following series : 0.6 + 0.6...
Text Solution
|
Find the sum to n terms of each of the following series : 1 + 4 + 1...
Text Solution
|