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If n(1), n(2), n(3),…..,n(100) are posit...

If `n_(1)`, `n_(2)`, `n_(3)`,…..,`n_(100)` are positive real numbers such that `n_(1)+n_(2)+n_(3)+…+n_(100)=20` and `k=n_(1)(n_(2)+n_(3)+n_(4))(n_(5)+n_(6)+…+n_(9))(n_(10)+….+n_(16))…(…+n_(100))`, then `k` belongs to

A

A. `(o,100]`

B

B. `(o,128]`

C

C. `(o,144]`

D

D. `(o,1024]`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Using `A.M ge G.M.`
`([n_(1)+(n_(2)+n_(3)+n_(4))+(n_(5)+n_(6)+...+n_(9))+...+(...+n_(100))])/(10) ge 10sqrt(k)(AM ge GM)`
`implies 2 ge 10 sqrt(k)`
`implies 0 lt k le 1024`
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