sequences-limits-help??

Question

Answer 1

(7.a)

Step 1:

The sequence function is .

Now find the number of terms (upto 10)to be plotted.

Step 2:

Plot the evaluated terms

So from the graph as approaches from the right side , the sequence approaches to 1.

Solution :

As approaches from the right side , the sequence approaches to 1.

Answer 2

(7.b)

Step 1:

The sequence function is .

Now find the number of terms (10 to 20 )to be plotted.

Step 2:

Plot the evaluated terms

So from the graph as approaches from the right side , the sequence approaches to 1.

Solution :

As approaches from the right side , the sequence approaches to 1.

Answer 3

(7.c)

Step 1:

From the above two results we can conclude that as approaches from the right side, the sequence approaches to 1.

Now verify it analytically.

Apply infinite limit to the sequence.

As tends , the sequence approaches to 1.

Solution :

The sequence approaches to 1.