Section Summary

We began this section by considering geometric sums and the compact formulas for them — with no ellipses. For example, if `r != 1`, then

These sums and the simple formulas for them will be especially important later in this chapter.

Next we extended the notation for limiting values first introduced in Section 9.2. From that section and this one we now have notation for

• limiting behavior of a function `f` as the independent variable goes to infinity:

  lim x → ∞ f ( x ) ,

• limiting behavior of a function `f` as the independent variable goes to negative infinity:

  lim x → - ∞ f ( x ) ,

• limiting behavior of a discrete sequence with terms `t_n`:

  lim n → ∞ t n ,

• limiting behavior of a function `f` as the independent variable approaches a finite number `a` — from both sides, if `a` is not an endpoint of the domain:

  lim x → a f ( x ) .

In the exercises we will introduce similar notation for

• limiting behavior of a function as the independent variable approaches a finite number from one side or the other, and

• behavior of a function going to `oo` or `-oo` as the independent variable approaches a number or goes to `oo` or `-oo`.