Question 112572
This infinite series is just another way of saying
{{{.88888888888}}}... on and on forever and ever. In the 
problem, they just pulled out each {{{8}}}, so they got
{{{.8 + .08 + .008 + .0008}}}... on and on forever
Believe it or not, {{{.88888888888}}}... ={{{8/9}}}
You find it with a little trick.
First call the repeating decimal {{{n}}}.
Then show what {{{10n}}} is
{{{10n = 8.88888888}}}...
{{{n = .888888888}}}...
subtract {{{n}}} from {{{10n}}}. Everything to the right of the 
decimal points cancel out. I'm left with
{{{9n = 8}}}
{{{n = 8/9}}}answer
OK, what if you had {{{.137137137137137}}}... on and on and on?
What's the value? Use the same trick a little differently
{{{1000n = 137.137137137137}}}...
{{{n = .137137137137137}}}...
now subtract
{{{999n = 137}}}
{{{n = 137/999}}}answer