If n harmonic means are inserted between 1 and r, then

Question

Question

This question was previously asked in

RPSC 2nd Grade Mathematics (Held on 4th July 2019) Official Paper

Answer 1

Given:
Harmonic Means between 1 and r, i.e.,

Harmonic Progression (H.P.) = 1, H1, H2, H3, ... , Hn, r

Concept:

where, , is the difference

here, z = last term of H.P., a = first term of H.P, n = no. of terms between a and z.

Calculation:
Here, z = r and a = 1

For n = 1 (first mean);

⇒ ------(1)

For n = n (nth mean);

⇒ ------(2)

from equations (1) and (2), we get

⇒

Therefore we get the solution,

⇒