Chapter B, Problem 19AYU

To determine

To find: Determine whether each sequence converges or diverges. If it converges, find its limit.

Answer to Problem 19AYU

Solution:

The given sequence converges. The limit is 4.

Explanation of Solution

Given:

$\left\{c_n\right\} = \left\{4 + \frac{{\left(-1\right)}^n}{n}\right\}$

Calculation:

$\left\{c_n\right\} = \left\{4 + \frac{{\left(-1\right)}^n}{n}\right\}$

Hence the sequence converges. Therefore we will find the limit

$\underset{n\to \infty }{\lim }{c}_n=\underset{n\to \infty }{\text{lim}}\left\{4+\frac{{\left(-1\right)}^n}{n}\right\}=4$