Talk:Ratio test

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[edit] radius of convergence

I removed anything about the radius of convergence because it wasn't clear. This test has a similar form when used for radius of convergence but aren't the same. Fresheneesz 01:58, 29 March 2006 (UTC)

[edit] unclarity

The edits by user:Fresheneesz made the article very unclear. It said:

In mathematics, the ratio test is a test (or "criterion") for the convergence of a series whose terms are real or complex numbers. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test. The ratio test is defined as:
L = \lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|
where
lim denotes the limit as n goes to infinity,
an and an+1 are the nth and (n+1)th terms of an infinite series
and
L is a label for the result of the ratio test.
The results of the ratio test show that:
  • if L<1 \! the series converges absolutely, or
  • if L>1 \! the series diverges, or
  • if L=1 \! the test is inconclusive (there exist both convergent and divergent series that satisfy this case).
For example, any series in the form:
\sum_{n=1}^\infty f_n
can be applied to the ratio test.

So it began by saying that the test is a particular number. That is nonsense.

It said "the results of the test show that" when it meant "the test states that".

It said "or" where it meant "and".

It said that a series can be applied to the test, where it meant the test can be applied to a series.

It said of a particular form, and offered this as an example, but the particular form was not a particular form, but completely general: ALL series are of that form. This does not constitute an "example". But the sentence began by saying "For example, ...".

It said "... where ... an and an+1 are the nth and (n+1)th terms of an infinite series". That infinite series was the topic of the whole account of what the test says; to relegate this to a "where..." clause that appears only AFTER the limit L is mentioned is objectionable on several levels, logical and pedagogical.

I mention all this here lest anyone consider reverting my edits.

I was led to this by a comment at talk:radius of convergence under the heading "odd wording". That led me to edit root test and then to edit the present article. Michael Hardy 22:14, 31 October 2006 (UTC)

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