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Chapter 7. Sequences and Series

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  • Chapter 7. Sequences and Series

    7.1 Infinite sequences

    Consider an infinite sequence of numbers like 1/2, 2/3, 3/4, 4/5, ... We want to define this as approaching 1, or “converging to 1.” The way to do this is to make a function f(n), which is only well defined for integer values of n. Then f(1)=1/2, f(2)=2/3, and in general f(n)=n/(n+1). With just a little tinkering, our definitions of limits can be applied to this type of function (see problem 1 on page 114).