Mathematics

Problem

Consider the sequence,

b_n

, defined recursively as follows:

b_1 = 3

b_2 = 2

, and

b_n = \frac{b_{n-1}}{b_{n-2}}

<br>&emsp;a. Complete the table below:

$b_1$	$b_2$	$b_3$	$b_4$	$b_5$	$b_6$	$b_7$	$b_8$	$b_9$

| 3 | 2 | | | |

\frac{3}{2}

| | | |<br>&emsp;<br>&emsp;b. Using your work from part (a), evaluate the series below.

\sum_{n=7}^{73} b_n