Explain the behavior of the sequence from the first problem in these notes using what you know about how computers store numbers in double precision.

x

n

$+$

$1$

$=$

$\{$

$2$

x

n

$,$

x

n

in

$[$

$0$

$,$

$1$

$2$

$]$

$2$

x

n

$$

$1$

$,$

x

n

in

$($

$1$

$2$

$,$

$1$

$]$

with

x

$0$

$=$

$1$

$10$

In particular, now that you know about how numbers are stored in a computer, how long do you expect it to take until the truncation error creeps into the computation?