Talk:Geometric sequence/Draft

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:

$1,0,0$

$0,0,0$

$0,0,1$

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 $a_{i-1}a_{i+1}=a_{i}^{2}$, 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

${a_{i+1} \over a_{i}}=q$

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)

Indeed. But not only since the last corrections -- q=1 was never excluded. It seems we both have overlooked it. But I have written it (blushing). --Peter Schmitt 15:55, 12 May 2010 (UTC)

For non-experts, article needs many more examples

It seems to me that, for non-experts, Geometric sequence needs many more examples, perhaps duplicate/triplicate examples in some cases. To make it more of a teaching tool for high-schoolers, undergraduates, other groups.

Why sequence called 'geometric'?

Would note vote against approving as is, but would hope for re-approval soon after. Anthony.Sebastian 02:43, 14 May 2010 (UTC)

1. Sorry, I do not understand what kind of examples do you mean. Would you please explain? And what do you mean by duplicate?

2. I guess, what you really want to see here is a "Tutorial" subpage. But this could wait for version 2. Boris Tsirelson 04:47, 14 May 2010 (UTC)

Sebastian, the name "geometrical" almost certainly comes from the geometrical interpretation of "proportional" (similar figures), but to include this guess would be hasty. A historical note -- either here or in a separate article -- would be nice to have, but I could not provide it without some thorough research.

As for more examples: What would they add? I agree that a main page should be as accessible as its topic allows. But an encyclopedia is not a teaching tool -- it is a handbook that should make it easy to find information. Thus it should tell its "story" with as many words as needed, but not with more. (I also confess that I would not know what to do in a Tutorial, either. The only topic I can think of are financial examples, but these would better fit to a page on interest.) --Peter Schmitt 15:14, 14 May 2010 (UTC)