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Q.

If S denotes the sum to infinity and Sn, the sum of n terms of the series1+12+14+18+⋯, such that S−Sn<11000 then the least value of n is

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a

11

b

8

c

10

d

9

answer is D.

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Detailed Solution

We have
S=11−12=2Sn=1−1/2n(1−1/2)=21−12n=2−12n−1∴ S=Sn<11000⇒12n−1<11000⇒ 2n−1>1000⇒ n−1≥10⇒ n≥11
Hence, the least value of n is 11.

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