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For a positive integer `n` let `a(n)=1+1/2+1/3+1/4+.....+1/((2^n)-1)dot` Then `a(100)lt=100` b. `a(100)dot> 100` c. `a(200)lt=100` d. `a(200)lt=100`

A

`a(100)gt100`

B

`a(100)lt 200`

C

`a(200) le 100`

D

`a(200)gt100`

Text Solution

Verified by Experts

The correct Answer is:
D
It can be proved with the help of mathematical induction that
`(n)/(2)lt a(n)le n`
`rArr (200)/(2)lt a(200)`
`rArr a(200)gt100`
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