# Series: The Series Finale Quiz

Think you’ve got your head wrapped around Series? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. The graph below shows the first 4 terms of the series

.

What is the third partial sum S3 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) |an + 1| < |an|
(III) |an + 1| > |an|
(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