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If S denotes the sum to infinity and Sn ...

If `S` denotes the sum to infinity and `S_n` the sum of `n` terms of the series `1+1/2+1/4+1/8+ ,` such that `S-S_n<1/(1000),` then the least value of `n` is `8` b. `9` c. `10` d. 11

A

8

B

9

C

10

D

11

Text Solution

Verified by Experts

We have
`S=1/(1-1/2)=2`
`S_(n)=((1-1//2^(n)))/((1-1//2))=2(1-1/2^(n))=2-1/(2^(n-1))`
`thereforeS-S_(n)lt1/1000`
`rArr1/(2^(n-1)lt1/1000`
`rArr2^(n-1)gt1000`
`rArrn-1ge10`
`rArrnge11`
Hence, the least value of n is 11.
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