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

Question

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

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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29