Question

Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent?

Answer 1

Step 1:

The sequence is .

The n^th term representation of the sequence is .

The partial sum of the sequence for n terms is .

Now tabulate the partial sum for different values of n.

The sum of first eight terms of the sequence is .

Answer 2

Contd......

Step 2:

Observe the partial sum of sequence, .

The partial sum appears to be increasing.

So the sequence is divergent.

Solution :

The sequence is divergent.