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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).