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 :

Explanation

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.