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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 thata 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 thatneither (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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