Suppose p is the first of `n(ngt1)` arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers.
The value of q is

Options

A. `((n-1)ab)/(nb+a)`
B. `((n+1)ab)/(nb+a)`
C. `((n-1)ab)/(na+b)`
D. `((n-1)ab)/(na+b)`

Answer

B

Explanation

For `ngt1`, we have `n+1gtn-1`
`implies (n+1)/(n-1)gt1 implies p((n+1)/(n-1))^(2)gtp" " [:.pgt0]".......(i)"`
Now, `p=a+d`
Since,a,p,b are in AP.
And `d=(b-a)/(n+1)`
`(1)/(q)=(1)/(a)+D=(1)/(a)+((1)/(b)-(1)/(a))/(n+1)`
`implies q=(ab(n+1))/(a+bn)`.