Chapter B, Problem 17AYU

To determine

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

Answer to Problem 17AYU

Solution:

The given sequence converges. The limit is 3.

Explanation of Solution

Given:

$\left\{b_n\right\} = \left\{3 - \frac{2}{n}\right\}$

Calculation:

$\left\{b_n\right\} = \left\{3 - \frac{2}{n}\right\}$

Hence the sequence converges. Therefore we will find the limit

$\underset{n\to \infty }{\lim }{b}_n=\underset{n\to \infty }{\text{lim}}\left\{3-\frac{2}{n}\right\}=3$