Does it appear that the series is convergent or divergent?

Question

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why.

Answer 1

Step 1:

The series .

Consider and .

The partial sum of the sequence for n  terms is .

Now tabulate the partial sum for different values of n.

Step 2:

Graph:

Plot the points of sequnce of terms corresponds to value with the blue dots.

Plot the points of partial sums corresponds to the with pink dots.

 

Step 3:

Divergence test:For the series , If , then the series is divergent.

Find

If

Since , then the series is divergent.

Solution:

The series is divergent.