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For a positive integer n, let a(n)=1+(...

For a positive integer n,
let `a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+ . . .+(1)/(2^(n)-1)` Then:

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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