If nine arthimatic means and nine harmonic means are inserted between 2 and 3 alternatively, then prove that A+6/H=5 (where A is any of the A.M.'s and H the corresponding H.M)

Explanation

`H_1,H_2,H_3 .........H_9` are 9 H.M

`A_1, A_2, A_3, ......... A_9`are 9 A.M

`2, H_1, H_2,.......3` H.P

`1/2 , H_1 ,H_2 , .....,1/3` AP

`D= (2-3)/((9+1)*2*3) = -1/60 as D= (a-b)/((n+1)*a*b)`

`as, 1/H_i = 1/2 + i*D`

`= 1/2 - i/60 `

`6/H_i = 3- i/10`

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