>
>Its value is exactly 1.

So I did a little digging, and found this link.
http://www.maths.abdn.ac.uk/~igc/tch/ma1002/appl/node57.html

However, all that is said about a converging series is that you can
determine a value that it approaches.  I see no requirement or statement
that it REACHES that value.

Here also,
http://forum.swarthmore.edu/dr.math/problems/may7.8.98.html

S = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n + ...

This series is described as convergent (obvious) and approaching 1, but not
described as being  equal to 1

Here:
http://www.misd.wednet.edu/~kim_schjelderup/Integrated%203/Pages/Seq&Series/4.7l%20Inifinite%20Series%20(WP).pdf

Finally the statement:
If the sequence of partial sums of an infinite series has a limit, then
that limit is the sum of the series.

Looks to me like we are defining "sum of the series" as something special,
and we are not saying that the series is equal to the limit, in a manner
similar to the way that "spin" is used in quantum mechanics.

It's certainly useful in calculation, because it causes those awkward
infinities to dissapear, by ignoring the infinitely tiny difference between
the actual result, and the defined result.

Inverting Zeno's paradox, the fallacy is that a finite distance (or number)
does not become infinite, simply because it can be divided into an infinte
number of smaller distances (or numbers)




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