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Question

If Sn=1+12+122+123+.........+12n1; Calculate the least value of n such that 2Sn<1100

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Solution

We can see that the terms are in G.P with first term 1 and the common ratio 12
Hence Sn=(12)n1121=2{2n1}2n=212n12Sn=12n1
Hence A/Q
12n1<11002n1>100n1>6n>7
Therefore, n=8

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