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

Series


Quizzes

1. The series  is→both 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?→
back to top