This morning Dream_Team brought up the age-old debate of whether
which of course it does.
Although this seems fairly conclusive, there is a much nicer (IMO) way.
One can treat the infintite decimal expansion as a geometric series.
Then it becomes apparent that the value of is equal to the sum to infinity of the geometric series.
And for a geometric series with common difference and first term
for explanation see below
This then prompted me to code some haskell, creating types for geometric and arithmetic series, but that post can come later.
Sum of Geometric Series
Now for the sum to infinity: