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If H1.,H2,…,H20 are 20 harmonic means be...

If `H_1.,H_2,…,H_20` are 20 harmonic means between 2 and 3, then `(H_1+2)/(H_1-2)+(H_20+3)/(H_20-3)=`

A

20

B

21

C

40

D

38

Text Solution

Verified by Experts

The correct Answer is:
C
`(H_(1)+2)/(H_(1)-2)+(H_(20)+3)/(H_(20)-3)=(1/2+1/H_(1))/(1/2-1/H_(1))+(1/3+1/H_(20))/(1/3-1/H_(20))`
`=(1/2+1/2+d)/(1/2-d-1/2)+(1/3+1/3-d)/(1/3+d-1/3)`
`=(1+d)/(-d)+(2/3-d)/d`
`=(2/3-1)/d-2`
`=2xx21-2` [as also,`1/3=1/2+21d`]
=40
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