If S dentes 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 lt 1/1000` then the least value of n is

Options

A. 8
B. 9
C. 10
D. 11

Answer

D

Explanation

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.