Chapter 8, Problem 1RCC

a.

To determine

To describe what is a convergent sequence.

Answer to Problem 1RCC

A convergent sequence are the sequence which has a limit and it approaches to a real number.

Explanation of Solution

Given information:

To describe what is a convergent sequence.

A convergent sequence are the sequence which has a limit and it approaches to a real number.

Example of convergent sequence is $\frac{1}{n}$ where $n=1,2,3,4,5,\mathrm{.........}$ .

The terms of $\frac{1}{n}$ are: $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{...........}$ and so on, and the sequenceconverges to 0, because the terms get closer and closer to 0.

b.

To determine

To describe what is a convergent series.

Answer to Problem 1RCC

A series is convergent if the sequence of its partial sums tends to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases.

Explanation of Solution

Given information:

To describe what is a convergent series.

A series is convergent if the sequence of its partial sums tends to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases.