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Quizzes

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

.

What is the third partial sum S3 of this series?𔾵

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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