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Find the harmonic mean of 1, 1/2, 1/3, 1...

Find the harmonic mean of 1, 1/2, 1/3, 1/n.

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Harmonic mean of 1, 1/2 and 1/3

x and y are two variables, such that y = (3)^(1/x) . If the harmonic mean of x is 3, find the geometric mean of y.

Knowledge Check

  • If H_1,H_2,H_3,.......H_n be n harmonic means between a and b then (H_1+a)/(H_1-a)+(H_n+b)/(H_n-b)=

    A
    0
    B
    n
    C
    2n
    D
    1

  • If between 1 and 1/31 there are n H.M's and ratio of 7th and (n-1)^th harmonic means is 9:5, then values of n is

    A
    12
    B
    13
    C
    5
    D
    14

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    The arithmetic mean of the numbers 1, 2, 3, ...., n is

    Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2 + 2^4) + 3/(1 + 3^2 + 3^4) + ...

    Insert : Let (x^(n+1) + y^(n+1))/(x^(n) + y^(n)) be the geometric mean of x and y , find n.

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