1.

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

Answer» `=1+1/2+1/4+1/8...+1/2^(n-1)`
there are total n terms
where a=1,r=1/2.
`=(a(1-r^n))/(1-r)`
Putting the values of a and r
`=(1(1-(1/2)^n))/(1-(1/2))`
`=2-1/2^(n-1)`
`2-1/2^(n-1)<2-1/1000`
`1/2^(n-1)>1/1000`
`2^(n-1)<1000`
`2^(n-1)=2^9`
`n-1=9`
`n=10`.


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