InterviewSolution
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InterviewSolution
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If `S_n = 1+1/2 + 1/2^2+...+1/2^(n-1) and 2-S_n < 1/100,` then the least value of `n` must be : |
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Answer» Given, `S_(n)=1+(1)/(2)+(1)/(2^(2))+"..."+(1)/(2^(n-1))=(1[*1-((1)/(2))^(n)])/((1-(1)/(2)))` ` implies S_(n)=2-(1)/(2^(n-1))` ` implies 2- S_(n)=(1)/(2^(n-1))lt(1)/(100)" "[therefore 2- S_(n)lt(1)/(100)]` `implies 2^(n-1)gt100gt2^(6)` `implies 2^(n-1)gt2^(6)` `therefore n-1gt6 implies ngt7` Hence, the least value of n is 8. |
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