(maths) sum of a series

Psyk · 21 May 2006 at 19:05

I came across the formular S=a/(1-r) in my notes but I can't figure out exactly what a and r are and how to find them. Can anyone explain?

Carzy · 21 May 2006 at 19:06

a is the start term and r is the ratio that the series increases by IIRC.

ballistic · 21 May 2006 at 19:07

you mean geometric series?
that's the formula as n approaches infinity

http://www.ies.co.jp/math/java/misc/sum/sum.html

Psyk · 21 May 2006 at 19:11

Ah ok I get it now. Would you believe this is degree level? Although I mean that in the loosest sense of the word.

ballistic · 21 May 2006 at 19:12

Psyk said:
Ah ok I get it now. Would you believe this is degree level? Although I mean that in the loosest sense of the word.

yeah I do, I had too use that formula many times for economics

daz · 21 May 2006 at 19:24

Stick 0.9 into a and for the ratio stick in 0.1.

0.9 + 0.09 + 0.009 etc.

0.9999 recurring does equal 1.

carvegio · 21 May 2006 at 19:29

Psyk said:
Ah ok I get it now. Would you believe this is degree level? Although I mean that in the loosest sense of the word.

No this is a-level stuff, normal maths. Not even further maths.

This would be assumed knowledge in a degree.

If we are talking about a maths degree

Royality · 21 May 2006 at 19:35

Yup, I'm doing A.S Maths (C2) and it's in that.

spirit · 21 May 2006 at 19:39

ballistic said:
yeah I do, I had too use that formula many times for economics

haha along with much more complicated stuff..

in fact this formula is used in as maths and as econ

carvegio · 21 May 2006 at 19:52

more importantly, do you understand it?

Need some help with some examples or a question? Just ask

Lagz · 21 May 2006 at 19:58

Psyk said:
Ah ok I get it now. Would you believe this is degree level? Although I mean that in the loosest sense of the word.

I can believe that you need this in a degree yes. What I cant believe is that you are doing a degree whilst not being resourceful enough to use google. How on earth do you normally look stuff up when you are confused?!

SaBBz · 21 May 2006 at 20:02

daz said:
Stick 0.9 into a and for the ratio stick in 0.1.

0.9 + 0.09 + 0.009 etc.

0.9999 recurring does equal 1.

Although I agree it does equal 1, is that formula not still an approximation?

Lagz · 21 May 2006 at 20:18

SaBBz said:
Although I agree it does equal 1, is that formula not still an approximation?

I dont think so, since it comes from the formula for the finite geometric series (which isn't an approximation) when you tend one of the values to 0.

Grrrrr · 21 May 2006 at 20:22

SaBBz said:
Although I agree it does equal 1, is that formula not still an approximation?

Nope. It's precise

The formula for a geometric series is

Code:

[U]a(1 - r^(n-1))[/U]
   1 - r

this equation is precise (working out can be found here http://en.wikipedia.org/wiki/Geometric_progression). The equation from the OP is derived from this by taking the limit as n -> infinity

Ricochet J · 21 May 2006 at 20:40

Grrr, it's r raised to the power of n-1, not n+1

Psyk · 21 May 2006 at 20:45

carvegio said:
No this is a-level stuff, normal maths. Not even further maths.

This would be assumed knowledge in a degree.

If we are talking about a maths degree

Well luckily for me we aren't

It was just an open option. I think I did it for A-level too. The unit I'm on doesn't go much beyond maths+further maths A-levels.

Lagz said:
I can believe that you need this in a degree yes. What I cant believe is that you are doing a degree whilst not being resourceful enough to use google. How on earth do you normally look stuff up when you are confused?!

Well first port of call is lecture notes. It was used but not explained in those. Then I checked wikipedia and I couldn't find it explained on there. I tried googling it but it came up with completely useless results.

Lagz · 21 May 2006 at 20:48

Psyk said:
I tried googling it but it came up with completely useless results.

If you type "sum of a series" into google nearly every link on the first page has the answer in it :S. Oh well, I'll shut up.

Psyk · 21 May 2006 at 20:51

Lagz said:
If you type "sum of a series" into google nearly every link on the first page has the answer in it :S. Oh well, I'll shut up.

Ok now I think about googling the actual formula probably wasn't the smartest idea

Oh well if my brain was on top form at the moment I would have probably been able to remember it anyway.

spirit · 21 May 2006 at 21:03

Psyk said:
Then I checked wikipedia and I couldn't find it explained on there. I tried googling it but it came up with completely useless results.

http://en.wikipedia.org/wiki/Geometric_series

?

Psyk · 21 May 2006 at 21:05

spirit said:
http://en.wikipedia.org/wiki/Geometric_series

?

Didn't know it was specifically about geometric series before. I did look up series but I couldn't find that page.