Answer
The total amount to pay for the room and board for 30 days is $\$10,737,418.23$.
Work Step by Step
In modeling this situation with a geometric sequence, $a_{1} = 0.01$ and $r = 2$, the general term is $a_{n} = 0.01(2)^{n-1}$ where n is the number of days charged.
The total amount to pay for the room and board for 30 days is
$\sum\limits_{n=1}^{30} a_{n} = \sum\limits_{n=1}^{30} 0.01(2)^{n-1}$
= $\frac{(0.01)(1 - 2^{30})}{(1 - 2)}$
= $\$10,737,418.23$
