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Sequences & Series

A sequence is a special kind of function whose domain is the positive integers. The

range of a sequence is the collection of terms that make up the sequence. Just asthe word sequence implies, the order of the terms in a sequence is important. The

first term of a sequence, for example, is found by taking the value of the function

at 1 ; the second term is the value of the function at 2 , and so on. Consider the

sequencef(x) =x. The terms of the sequence, denoted a1, a2, a3,,anare 1, 2,

3,,n. When working with sequences, instead of using function notation to

express the formula of the function, a formula is the following form is

used: an= n. This is the same sequence as above, but the conventional nis used to

denote an integer, since only integers are in the domain of sequences. Two

important categories of sequences are arithmetic sequences, and geometric

sequences. Both are examples of a recursive sequence--a sequence in which each

term (besides the first) depends on the previous term. Both of these types of

sequences will be discussed.

When the terms of a sequence are summed, the result is called a series. Some series

increase without bound as nincreases, but others approach a limit. Both types of

series will be studied in the following sections. There are also certain formulas for

calculating the limits of series that we'll learn. The study of series is an importantpart of calculus, and it all starts with sequences.

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Summary

Quinine was the first effective Western treatment formalariacaused

byPlasmodium falciparum,appearing in therapeutics in the 17th

century. It is pre-dated as a malarial treatment by the Chinese herbalist'suse of Artemisia Annua, described in a 4th-century text, a plant from

which the antimalarial drugArtemisininwas derived. It remained the

antimalarial drug of choice until the 1940s. When a person is given a

dosage of quinine, the body metabolizes most of the quinine. With the

application of mathematics or to put it more precisely the methods of

sequences and series, it is possible to calculate the amount of quinine in

the body right after every dosage is given to a malaria patient. The

concentration of quinine plays a crucial part contributing to theeffectiveness of the treatment. Not only that when the concentration of a

dosage quinine is too high, it is claimed hazardous to the patient. Thus,

with the help of mathematics, all these problems above can be solved by

applying the right methods and formula.

http://en.wikipedia.org/wiki/Malariahttp://en.wikipedia.org/wiki/Malariahttp://en.wikipedia.org/wiki/Malariahttp://en.wikipedia.org/wiki/Plasmodium_falciparumhttp://en.wikipedia.org/wiki/Plasmodium_falciparumhttp://en.wikipedia.org/wiki/Plasmodium_falciparumhttp://en.wikipedia.org/wiki/Artemisininhttp://en.wikipedia.org/wiki/Artemisininhttp://en.wikipedia.org/wiki/Artemisininhttp://en.wikipedia.org/wiki/Artemisininhttp://en.wikipedia.org/wiki/Plasmodium_falciparumhttp://en.wikipedia.org/wiki/Malaria