This morning *Dream_Team* brought up the age-old debate of whether

which of course it does.

### Method 1

Although this seems fairly conclusive, there is a much nicer (IMO) way.

### Method 2

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

So for

VoilĂ .

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:

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Lame, everyone knows that

1 – 0.99999… = 0.00000….1