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If S(n)=1+(1)/(2)+(1)/(2^(2))+"..."+(1)/...

If `S_(n)=1+(1)/(2)+(1)/(2^(2))+"..."+(1)/(2^(n-1))`, then calculate the least value of n such that `2-S_(n)lt(1)/(100)`.

A

`8`

B

`7`

C

`9`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
A
If `S_(n) = 1+(1)/(2)+` …………
`S_(n) = ((1-((1)/(2))^(n)))/(1-(1)/(2))`
`S_(n)=2-((1)/(2))^(n-1) implies ((1)/(2))^(n-1) lt (1)/(100)`
`implies n-1 ge 7 implies n ge 8`
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