# Chapter 7. Sequences and Series

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- 148371

# 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).