Question

Three hormonic mean if 1/13 and1/19 are
The three hormonic means b/w 1/3 and1/19

Answer 1

Answer:-

We know that,

Harmonic mean (H.M) between two numbers a & b is 2ab/(a + b).

Harmonic mean between 1/13 , 1/19 = [2(1/13)(1/19)]/1/13 + 1/19

→ H.M of 1/13 & 1/19 = (2/247)/(19 + 13)/247

→ H.M = (2/247)* (247/32)

→ H.M = 1/16

Now,

1/13 , 1/16 , 1/19 are in HP.

→ H.M of 1/13 , 1/16 = 2(1/13)(1/16)/(1/13 + 1/16)

→ H.M = (2/208)/(16 + 13)/208

→ H.M = (2/208)*(208/29)

→ H.M = 2/29

1/13 , 2/29 , 1/16 , 1/19 are in HP.

→ H.M of 1/16 , 1/19 = 2(1/16)(1/19)/(1/16 + 1/19)

→ H.M = (2/304)/(19 + 16)/304

→ H.M = (2/304)*(304)/35

→ H.M = 2/35.

Hence, the three harmonic means between 1/13 and 1/19 are 1/16 , 2/29 , 2/35.