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

If S denote the sum to infinity and `S_n`, the sum of n terms of the series `1+1/3+1/9+1/27+....` such that `S-S_n lt 1/300`, then the least value of n is

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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