- #51

Mark44

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Just for the sake of accuracy, your LaTeX script was almost correct. Here is what I'm sure you meant.By the way,anynumber, whether it has recurring decimals or not, can be written as an infinite series in aninfinitenumber of ways, e.g. [tex]1 = \sum^\infty_{n=1}\frac{1}{2n}[/tex]

The value of that sum is exactly 1. The fact that a human being manually summing up the numbers would never 'reach' 1 doesn't enter into it. You're not making anything clearer by saying that, you're bringing up exactly what gets people mixed up.

[tex]1 = \sum^\infty_{n=1}\frac{1}{2^n}[/tex]

The sum as previously written does not add to 1. In fact, the sequence of partial sums can be shown to be increasing without bound.