Chapter 8: Q8E (page 443)
Determine whether the geometric series is convergent or divergent..If it is convergent,find its sum.
\(2 + .5 + .125 + 0.03125 + ......\)
The given series is convergent and Sum=\(\frac{8}{3}\)
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Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = {2^{ - n}}\cos n\pi \)
\({\sum\limits_{k = 1}^\infty {\left( {\cos (1)} \right)} ^k}\) Find Whether It Is Convergent Or Divergent. If It Is Convergent Find Its Sum.
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = \ln (n + 1) - \ln n\)
After injection of a dose D of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as \(D{e^{ - at}}\), where t represents time in hours and a is a positive constant.
(a) If a dose \(D\) is injected every \(T\) hours, write an expression for the sum of the residual concentrations just before the \((n + 1)\)st injection.
(b) Determine the limiting pre-injection concentration.
(c) If the concentration of insulin must always remain at or above a critical value \(C\), determine a minimal dosage \(D\) in terms of \(C\) , \(a\), and \(T\).
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = \left\{ {\frac{{(2n - 1)!}}{{(2n + 1)!}}} \right\}\)
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