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Series

Series

Series: The Series Finale True or False

1. The graph below shows the first 4 terms of the series

.

What is the third partial sum S3 of this series? -> 1

2. Consider the two series  and .

If

and

,

the divergence test tells us that -> a diverges and B may either diverge or converge.

3. Consider the series . In order to use the Alternating Series Test, which of the following conditions must apply?

(I)  must be an alternating series
(II) |an + 1| < |an|
(III) |an + 1| > |an|
(IV) \ -> I, II, and IV

4. Consider the alternating series

What is the error bound for the 5th partial sum? ->

5. Which series can not have its convergence or divergence determined by using the ratio test? ->
6. Consider the picture shown below.

Assume that  diverges and  converges.

Which of the following statements is true? -> The series  converges.

7. Consider two series:

(I)
(II) 

By using the comparison test with the harmonic series for comparison, we can show that -> neither (I) nor (II) diverge

8. Suppose  and  both converge. Then -> converges
9. Which convergence/divergence test should be tried first? -> the divergence test
10. The series  -> diverges by comparison with 

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