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Liquidxlax
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Homework Statement
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 a pure as you like, but if n=3, at least one-half of the impurity remains no matter how many stages are used.
Homework Equations
may be relevant, Sn = (ao(1-rn)/(1-r))Sn-rSn = (ao-aor^n)
The Attempt at a Solution
well i figured out the series expansion for bothSUM (1/(n^2 -n)) (sorry i couldn't figure out the text thing)n=2 gives = 1/2 + 1/6 + 1/12 + 1/20 + ...
n=3 gives = 1/6 + 1/12 + 1/20 + 1/36 + ...
I know the sum of n=2 is pretty much 1 and n=3 is pretty much 1/2. My real problem is i can't figure out how to get it into:Sn = (ao(1-rn)/(1-r))so I can differentiate to get the sum. Any help would be appreciated and thanks for helping a noob