# Series

# Series: The Series Finale Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Series**Q. The graph below shows the first 4 terms of the series

.

What is the third partial sum *S*_{3} of this series?

1

2

4

7

Q. Consider the two series and .

If

and

,

the divergence test tells us that

Both

*a*and*B*converge.*a*diverges and

*B*converges.

*a*diverges and

*B*may either diverge or converge.

*a*may either diverge or converge and

*B*converges.

Q. 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) |*a*_{n + 1}| < |*a _{n}*|

(III) |

*a*

_{n + 1}| > |

*a*|

_{n}(IV) \

I only

I and IV

I, II, and IV

I, III, and IV

Q. Consider the alternating series

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

Q. Which series can not have its convergence or divergence determined by using the ratio test?

Q. Consider the picture shown below.

Assume that diverges and converges.

Which of the following statements is true?

The series converges.

The series diverges.

The series converges.

The series diverges.

Q. Consider two series:

(I)

(II)

By using the comparison test with the harmonic series for comparison, we can show that

(I) diverges

(II) diverges

both (I) and (II) diverge

neither (I) nor (II) diverge

Q. Suppose and both converge. Then

converges

The series converges.

both and converge

we do not know if either or converge

Q. Which convergence/divergence test should be tried first?

the divergence test

the ratio test

the integral test

the comparison test

Q. The series

converges by comparison with

diverges by comparison with

converges by comparison with

diverges by comparison with