Chapter B, Problem 20AYU

In Problems 5-28, determine whether each sequence converges or diverges. If it converges, find its limit.

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

To determine

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

Answer to Problem 20AYU

Solution:

The given sequence converges. The limit is 0.

Explanation of Solution

Given:

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

Calculation:

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

Hence the sequence converges. Therefore we will find the limit

$\underset{n\to \infty }{\lim }{c}_n=\underset{n\to \infty }{\text{lim}}\left\{\frac{1+{\left(-1\right)}^n}{n}\right\}=0$