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Series

Series

Series: Burgers and Hotdogs: The All Star Examples of Mathematical Series 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 series  is


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


Q. Find


The sum doesn't exist because |r| > 1.
Q. The sum of the infinite geometric series

,

where a ≠ 0, is



 for all r
 for |r| < 1, undefined otherwise
 for |r| ≤ 1, undefined otherwise
 for -1 ≤ r < 1, undefined otherwise
Q. Find .


1
Q. Let a be a constant. If the series  converges then we must have


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 =


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?


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