Home
Class 11
MATHS
If H1, H2, ,H(20)a r e20 harmonic means...

If `H_1, H_2, ,H_(20)a r e20` harmonic means between 2 and 3, then `(H_1+2)/(H_1-2)+(H_(20)+3)/(H_(20)-3)=` a. 20 b.21 c. 40 d. 38

A

20

B

21

C

40

D

38

Text Solution

Verified by Experts

`(H_(1)+2)/(H_(1)-2)+(H_(20)+3)/(H_(20)-3)=(1/2+1/H_(1))/(1/2-1/H_(1))+(1/3+1/H_(20))/(1/3-1/H_(20))`
`=(1/2+1/2+d)/(1/2-d-1/2)+(1/3+1/3-d)/(1/3+d-1/3)`
`=(1+d)/(-d)+(2/3-d)/d`
`=(2/3-1)/d-2`
`=2xx21-2` [as also,`1/3=1/2+21d`]
=40
Promotional Banner

Similar Questions

Explore conceptually related problems

If H_(1) , H_(2) are two harmonic means between two positive numbers a and b , (a != b) , A and G are the arithmetic and geometric means between a and b , then (H_(2) + H_(1))/(H_(2) H_(1)) is

If H is the harmonic mean between Pa n dQ then find the value of H//P+H//Qdot

If x_1,x_2 …,x_(20) are in H.P and x_1,2,x_(20) are in G.P then Sigma_(r=1)^(19)x_rr_(x+1)

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

What is the relation between h_(1),h_(2) , u and v.

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, find an expression for the geometric mean of G_(1), G_(2),...,G_(n) in terms of A_(1), A_(2),...,A_(n), H_(1), H_(2),..., H_(n)

If A_(1) , A_(2) , A_(3) , G_(1) , G_(2) , G_(3) , and H_(1) , H_(2) , H_(3) are the three arithmetic, geometric and harmonic means between two positive numbers a and b(a gt b) , then which of the following is/are true ?