Math Is Fun Forum

shubhamrathi

Member

Registered: 2010-09-17

Posts: 2

Need help with progression and series

please read the following extract
" Algebraically, we can represent the n terms of the geometric series, with the first term a, as:
Sn=a+ar+ar^2+ar^3+...ar^n-1 [1]
Each term is the previous term times r, so we can try multiplying the series by r
rSn=ar+ar^2+ar^3+...+ar^n-1+ar^n [2]
Subtracting Equation 2 from Equation 1, we get:
(1-r)Sn=a-arn  "

Here in [1]- i dont understand why we stop at ar^n-1 when we have to find the sum of terms upto 'n' &
in [2]-what is the effect of adding r to the series and also why here have we extended the term upto ar^n but not in [1]
Kindly elaborate.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help with progression and series

Hi shubhamrathi;

2) Is just 1) with both sides multiplied by r.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

shubhamrathi

Member

Registered: 2010-09-17

Posts: 2

Re: Need help with progression and series

I understand that its multiplied by 'r'. But why do we stop the series and n-1?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help with progression and series

Hu shubhamrathi;

You can stop it anywhere you want. It is a generic series. By stopping it at n-1 you n terms.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.