A dosage d of a drugis given at times t=0,1,2.... The drug decays in the bloodst

Question

A dosage d of a drugis given at times t=0,1,2.... The drug decays in the bloodstream exponentially with rate p. Thus, the amount in the bloodstream after t+1 doses is

d+de^-p+de^-2p+de^-3p+...+de^-tp+..

Suppose the situation were continued "Infinitely". Would the above infinite series converge? if so can we find a value to which it converges to(t-->infinity)?

What would such a value mean in the context of the problem?

If p=.1 find the dosage needed to maintain a drug level at 2.

Please answer all questions please and show all your work please. thank you so much!!! 5 stars to best answer. Also pease do not give me the answer i asked before i want a better answer with work and explanation.

Explanation / Answer

here an = de^-n-np

an+1 = de^-(n+1)-(n+1)p

an+1/an = de^-n - np / de^-n- np - (p-d/e)/d/e^n - np

=1 - [ (pe-d)/d-np e^n) * e^n-1]

which is always <=1

hence sequence converges

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