© 2014 Shmoop University, Inc. All rights reserved.
Series

Series

Series: Burgers and Hotdogs: The All Star Examples of Mathematical Series True or False

1. The series  isboth an arithmetic and a geometric series
2. 0.5, 0.25, 0.125, ... is a(n)arithmetic series
3. The nth partial sum of a geometric series is
4. Find
5. The sum of the infinite geometric series

,

where a ≠ 0, is for |r| < 1, undefined otherwise

6. Find .
7. Let a be a constant. If the series  converges then we must have|a| < 1
8. We can write the decimal 0.421421421... as a rational number using an infinite geometric series with r =
9. Which of the following expressions could be considered to be in "closed form"?

(I) a + ar + ar2 + ... + arn – 1

(II) 

(III) (II) and (III)

10. 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?

Submit
Advertisement
Advertisement
Advertisement