- #1
vecsen
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Homework Statement
The question is : "In a water purification process, one-nth of the impurity is removed in the first stage.
In each succeeding stage, the amount of impurity removed is one-nth of that removed in the preceding stage. Show that if n = 2, the water can be made as pure as you like, but that if n = 3, [I take this to mean that 66.667% of impurities remaining--] at least one-half of the impurity will remain no matter how many stages are used. "
Homework Equations
I am thinking, granted, there will always be some residue, but that is what 'clean water is': one with only traces of other substances.
I tried at first on paper (with squares). The residue becomes vanishingly small.
As I mention in the title, I expect to be shown in error, but this seems monstrously improbable to me. For instance how is this different from, say 2% inflation? Suppose that--to use gov. statistics-- 98% on average of the value of money remains from year to year. After a century money will have lost ~95.245% of its initial value (there is a certain degree of realism here :).
The Attempt at a Solution
In short I am thinking more along the lines of (1-1/n)^k rather than a *( (1-r^k)/ 1-r). If by any chance I am right, whatever was that woman thinking of?
Any assistance would be greatly appreciated