Explain and answer #48 If the nth partial sum of a series sigma^_n = 1 a_n is S_

Question

Explain and answer #48

If the nth partial sum of a series sigma^_n = 1 a_n is S_n = n - 1/n + 1 find a_n and sigma^_n = 1 a_n. If the nth partial sum of a series sigma^_n = 1 a_n is S_n = 3 - n2^-n, find a_n and sigma^_n = 1 a_n. A patient is prescribed a drug and is told to take one 100-mg pill every eight hours. After eight hours, about 5% of the drug remains in the body. (a) What quantity of the drug remains in the body after the patient takes three pills? (b) What quantity remains after n pills are taken? (c) What happens in the long run? To control an agricultural pest called the medfly (Mediterranean fruit fly), N sterilized male flies are released into the general fly population every day. If s is the proportion of these sterilized flies that survive a given day. then Ns^k will survive for k days. (a) How many sterile flies are there after n days? What happens in the long run?

Explanation / Answer

48)

given sn =3-n2-n

an =sn -sn-1

an =(3-n2-n)-(3-(n-1)2-(n-1))

an =-n2-n +(n-1)2-(n-1)

an =(-n+2n-2)2-n

an =(n-2)2-n

[n=0 to ] an = lim[n->] sn

[n=0 to ] an = lim[n->] (3-n2-n)

[n=0 to ] an = lim[n->] (3-(n/2n))

[n=0 to ] an = (3-0)

[n=0 to ] an = 3

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