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 *n*th 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*| < 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* + *ar*^{2} + ... + *ar*^{n – 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 *n*th year?