Question

Insert three harmonic means between 1 and 7.
Please guys answer this question and I will mark your answer as BRAINLIEST ​

Answer 1

Answer:

14/11  ,  7/4   &   14/5

Step-by-step explanation:

For two numbers a & b

Harmonic mean = H

1/H = (1/a + 1/b)/2

=> H = 2/(1/a + 1/b)

=> H = 2ab/(b + a)

=> H = 2ab/(a + b)

a = 1  & b = 7

H = 2* 1 * 7/(1 + 7)

=> H = 7/4

Now find H between  1 & 7/4   *  7/4 & 7

H = (2 * 1 * 7/4)/(1 + 7/4)       &   (2*(7/4)*7)/(7/4 + 7)

= 14/11     & 98/35

= 14/11  & 14/5

Three harmin means are

14/11  ,  7/4   &   14/5

so Harmonic series is like this

1  , 14/11 , 7/4  , 14/5  , 7

or

14/14 , 14/11 , 14/8  , 14/5  , 14/2