Chapter B, Problem 28AYU

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

$\left\{a_n\right\}=\left\{\sin \left(n\pi -\frac{\pi }{2}\right)\right\}$

To determine

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

Answer to Problem 28AYU

Solution:

The given sequence diverges.

Explanation of Solution

Given:

$\left\{a_n\right\} = \left\{\sin \left(n\pi - \frac{\pi }{2}\right)\right\}$

Calculation:

$\left\{a_n\right\} = \left\{\sin \left(n\pi - \frac{\pi }{2}\right)\right\}$

${\lim }_{n \to \infty }{a}_n = \underset{n \to \infty }{\lim }\left\{\sin \left(n\pi - \frac{\pi }{2}\right)\right\} = \infty$

Hence the sequence diverges.