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 series
is
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_1.png)
an arithmetic series
a geometric series
neither an arithmetic nor a geometric series
both an arithmetic and a geometric series
Q. 0.5, 0.25, 0.125, ... is a(n)
arithmetic sequence
arithmetic series
geometric sequence
geometric series
Q. The nth partial sum of a geometric series is
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_2.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_3.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_4.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_5.png)
Q. Find
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_6.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_7.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_8.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_9.png)
The sum doesn't exist because |r| > 1.
Q. The sum of the infinite geometric series
,
where a ≠ 0, is
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_11.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_12.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_13.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_14.png)
Q. Find
.
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_15.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_16.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_17.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_18.png)
1
Q. Let a be a constant. If the series
converges then we must have
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_19.png)
a = 0
|a| < 1
0 < a < 1
-1 < a < 0
Q. We can write the decimal 0.421421421... as a rational number using an infinite geometric series with r =
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_20.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_21.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_22.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_23.png)
Q. Which of the following expressions could be considered to be in "closed form"?
(I) a + ar + ar2 + ... + arn – 1
(II)
(III)
(II) only
(III) only
(I) and (II)
(II) and (III)
Q. Every year Leopold puts $500 into his bank account and then earns 5% interest on the total contents of his account. At the end of the first year, his bank account contains $525. How many dollars are in his bank account at the end of the nth year?
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_26.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_27.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_28.png)
![](https://media1.shmoop.com/images/calculus/calc_series_quiz_2_latek_29.png)