Answer
$ a.\quad$
Diverges.
See image. Steps given below.
$ b.\quad$
Diverges.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9be68e45-febe-4f1a-a385-5ea2b705610f/result_image/1580597192.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240617%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240617T151526Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ab142d3d39842020d41eabad28ae63ed8722f1e4efcf254c0d53689b15207de6)
Work Step by Step
$a.\quad $
The steps you take will depend on the CAS you are using, but they follow the same logic.
Using the free online CAS at "geogebra.org/cas":
Cell 1: Enter the function representing the sequence
$a(x)=\sin x$
From the dropdown menu, select "Table of values".
In the dialog box for the table, set the range from 1 to 25, step 1.
When we observe the graph, the points alternate above/below the x-axis between values of y=-1 and y=+1.
The y coordinate does not seem to approach any certain fixed value.
The sequence seems to diverge.
In the next free cell of the CAS, we find the limit when $ n\rightarrow\infty$
Here, we enter "L=Limit(a, infinity)" (without quotes)
The CAS returns the limit to be " $?$ ".
(There is no limit)
$b.\quad $
The sequence diverges.
$ a.\quad$
Diverges.
See image. Steps given below.
$ b.\quad$
Diverges.