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

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

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If S denotes the sum to infinity and S_n, the sum of n terms of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots, such that S - S_{n} < \frac{1}{1000}$ then the least value of n is

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Correct option is D

We haveS=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≥11Hence, the least value of n is 11.

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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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If S denotes the sum to infinity and S_n, the sum of n terms of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots, such that S - S_{n} < \frac{1}{1000}$ then the least value of n is