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If harmonic mean of (1)/(2),(1)/(2^(2)),...

If harmonic mean of `(1)/(2),(1)/(2^(2)),(1)/(2^(3)),...,(1)/(2^(10))` is `(lambda)/(2^(10)-1)`, then `lambda=`

A

`10.2^(10)`

B

`5`

C

`5.2^(10)`

D

`10`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Given quantities are `(1)/(2),(1)/(2^(2)),(1)/(2^(3)),…,(1)/(2^(10))` ,brgt `H.M.=(10)/(2+2^(2)+2^(3)+...+2^(10))`
`=(10)/((2(2^(10)-1))/(2-1))=(5)/(2^(10)-1)`
`:.lambda=5`
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