Chapter B, Problem 15AYU

To determine

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

Answer to Problem 15AYU

Solution:

The given sequence converges. The limit is 0.

Explanation of Solution

Given:

$\left\{s_n\right\} = \left\{2{\left(\frac{4}{5}\right)}^n\right\}$

Calculation:

$\left\{s_n\right\} = \left\{2{\left(\frac{4}{5}\right)}^n\right\}$

Hence the sequence converges. Therefore we will find the limit

$\underset{n \to \infty }{\lim } s_n = \underset{n \to \infty }{\lim } \left\{2{\left(\frac{4}{5}\right)}^n\right\} = 0$