Chapter B, Problem 18AYU

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

$\left\{a_n\right\}=\left\{10+\frac{1}{n}\right\}$

To determine

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

Answer to Problem 18AYU

Solution:

The given sequence converges. The limit is 10.

Explanation of Solution

Given:

$\left\{a_n\right\} = \left\{10 + \frac{1}{n}\right\}$

Calculation:

$\left\{a_n\right\} = \left\{10 + \frac{1}{n}\right\}$

Hence the sequence converges. Therefore we will find the limit

$\underset{n\to \infty }{\lim }{a}_n=\underset{n\to \infty }{\text{lim}}\left\{10+\frac{1}{n}\right\}=10$