What is the greatest value of the positive integer n satisfying the condition `1+1/2+1/4+1/8+.....+1/2^[n-1]<2-1/1000` ?

Options

A. 8
B. 9
C. 10
D. 11

Answer

C

Explanation

` 1 + 1/2 + 1/ 4 + 1/8 + ........+ 1/(2^(n-1)) lt 2 - 1/1000`
LHS of given inequality is in G.P
` :. (1-1/(2^(n)))/(1-1/2)lt2 - 1/1000`
` rArr 2- 1/(2^(n-1)) lt 2- 1/ 1000`
` rArr 2^(n-1) lt 1000`
Now, `(2)^(9) = 512 & (2)^(10) = 1024`
` :. n-1 = 9 `
` rArr n=10`