Chapter 8.1, Problem 36E

To determine

To graph: Graph the given sequence, check whether it is convergent or divergent and guess the value of limit if the graph is convergent.

Answer to Problem 36E

The given sequence is convergent and the value of limit is $3$ .

Explanation of Solution

Given information: The sequence is $a_n=\sqrt{n}\sin \left(\frac{\pi }{\sqrt{n}}\right)$ .

Graph: The graph of the sequence is given below,

  

Interpretation: From the graph it is clear that the graph is bounded by line $y=3$ .

The graph of sequence is bounded so it is a convergent sequence.

It is bounded by line $y=3$ so the limit of the sequence is $3$ .

Hence, the given sequence is convergent and value of limit is $3$ .