30 Nov 2008

Infinite Sequences defined in Edwards & Penney

by Corry Shores
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"An infinite sequence of real numbers is an ordered, unending list

of numbers." The list is ordered, because it has a first term, a1, followed by a second term, a2, a third term a3, and so on. The sequence is unending (infinite) because for every n in the series, the nth term an has a sucessor an+1. Thus an infinite sequence never ends, even though we only represent part of it, and let the elipsis signify its infinite continuation. We might give more concise notations for the above sequence using:

Often an infinite sequence {an} can be described altogether by a single function f that gives each sucessive term in the sequence as the successive value of that function:

In this case above, the an = f(n) is the formula for the nth term of the sequence.

from Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, p.682c.d.

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