Talk:Geometric sequence/Draft: Difference between revisions

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imported>Peter Schmitt
imported>Boris Tsirelson
(→‎Dividing by zero: new section)
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::Nice. [[User:Boris Tsirelson|Boris Tsirelson]] 17:35, 11 May 2010 (UTC)
::Nice. [[User:Boris Tsirelson|Boris Tsirelson]] 17:35, 11 May 2010 (UTC)
== Dividing by zero ==
If ''q'' is permitted to be 1 then the formula for the finite sum needs a reservation. [[User:Boris Tsirelson|Boris Tsirelson]] 15:05, 12 May 2010 (UTC)

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 Definition In elementary mathematics, a (finite or infinite) sequence of numbers such that the quotient of consecutive elements is constant. [d] [e]
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Cannot resist

The term still reminds me of the order in which students entered the room for geometry class; I was generally last. --Howard C. Berkowitz 21:44, 9 January 2010 (UTC)

What about zero?

It is unclear for now, whether the following sequences are geometric or not:

Boris Tsirelson 10:10, 10 May 2010 (UTC)

Right. But what is meant by 0,0,1 ? --Peter Schmitt 16:52, 11 May 2010 (UTC)
Just a finite sequence, of length 3, whose first element is 0, second 0, and third 1. (You may think of a possible definition , but I did not say I want it to be in the article; I stay neutral; I only want some definition; and in fact, I feel already satisfied.) Boris Tsirelson 17:34, 11 May 2010 (UTC)
I see. I think it is best to stay with the "standard" (naive) definition here. That is why I did not change the lead, but only added a remark to the formal section. --Peter Schmitt 17:39, 11 May 2010 (UTC)

What about q?

"...is called geometric sequence if

for all indices i." — I'd add, "and some number q (not dependent on i)." Boris Tsirelson 10:16, 10 May 2010 (UTC)

Right. Done. --Peter Schmitt 16:53, 11 May 2010 (UTC)

More examples

An example of an infinite increasing sequence could be added. Also a constant sequence. Boris Tsirelson 10:20, 10 May 2010 (UTC)

I have added 3 more ( and 0,0,0 ). --Peter Schmitt 16:54, 11 May 2010 (UTC)
Nice. Boris Tsirelson 17:35, 11 May 2010 (UTC)

Dividing by zero

If q is permitted to be 1 then the formula for the finite sum needs a reservation. Boris Tsirelson 15:05, 12 May 2010 (UTC)