# Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one

Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one day later. Just after taking another dose of medication on the second day, the amount of medication in your blood equals the sum of the second dose and the fraction of the first dose remaining in your blood, which is m+mf. Continuing in this fashion, the amount of medication in your blood just after your nth does is $$\displaystyle{A}_{{{n}}}={m}+{m}{f}+\ldots+{m}{f}^{{{n}-{1}}}$$. For the given values off and m, calculate $$\displaystyle{A}_{{{5}}},{A}_{{{10}}},{A}_{{{30}}}$$, and $$\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}$$. Interpret the meaning of the limit $$\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}$$. $$f=0.25,$$ $$m=200mg.$$

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Usamah Prosser

$$\displaystyle{A}_{{{5}}}={266.4},$$

$${A}_{{{10}}}={266.66},$$

$${A}_{{{30}}}={266.67},$$

$$\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}={266.67}$$