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Question

If S denotes the sum to infinity and Sn the sum of n terms of the series 1+12+14+18+....., such that S−Sn<11000, then the least value of n is-

A
8
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B
9
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C
10
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D
11
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Solution

The correct option is D 11
By using Sum of GP =a(1rn)1r when r<1 we have

S=11(1/2)=2

Sn=1(1/2)n1(1/2)=212n1

SSn=12n1<11000 or 2n1>1000

Now 29=512

n1>9 or n>10

Hence the least value is 11.

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