Home
Class 12
MATHS
If nine arithmetic means and nine harmon...

If nine arithmetic means and nine harmonic means are inserted between 2 and 3 alternatively, then prove that `A+6//H=5` (where `A` is any of the A.M.'s and `H` the corresponding H.M.)`dot`

Text Solution

Verified by Experts

Let `H_(1),H_(2),..H_(9)` be nine harmonic means are inserted between 2 and 3 alternatively, then prove that A+6/H=5 (where A is any of the A.M.'s and H the corresponding H.M.).
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.74|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.75|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.72|1 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If one arithmetic mean A and two geometric means p, q be inserted between two given numbers, then prove that, (p^(2))/(q) + (q^(2))/(p) = 2A .

If one geometric mean G and two arithmetic means p, q be inserted between two given numbers, then prove that, G^(2) = (2p - q) (2q - p) .

Insert four H.M.’s between 2/3 and 2/13.

If H is the harmonic mean between P and Q then find the value of H//P+H//Qdot

If a and b are two positive numbers, then prove that A.M. ge G.M. ge H.M.

If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers , then prove that the value of q can not lie between p and ((n+1)/(n-1))^2p .

'n' A.M's are inserted between a and 2b, and then between 2a and b. If p^(th) mean in each case is a equal, a/b is equal to

If a is the A.M. of b and c and the two geometric mean are G_1 and G_2, then prove that G_1^3+G_2^3=2a b c

Insert two H.M.s between (-6) and (3)/(13) .

Prove that the sum of n arithmatic means between two numbers is n times the single A.M between them.