My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By v8archie
Reply
 
LinkBack Thread Tools Display Modes
October 26th, 2016, 07:20 AM   #1
Newbie
 
Joined: Oct 2016
From: UK

Posts: 7
Thanks: 0

Geometric Series Formula Proof Question

My textbook says:

Sn = u1 +u1r + u1r^(2) ...u1r^(n-2) + u1^(n-1)

rSn = u1r + u1r^(2) + u1r^(3) ...u1r^(n-1) +u1^(n)

rSn - Sn =u1r^(n) - u1

How can the above statement be true?

You can't simplify u1r - u1 or u1r^(2) - u1(r).

This would suggest that u1r^(n) - u1r^(n-1) = u1r^(n) - u1, which isn't true.

Could somebody explain how the statement rSn - Sn is true?

Last edited by Tomedb; October 26th, 2016 at 07:26 AM.
Tomedb is offline  
 
October 26th, 2016, 08:27 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,636
Thanks: 2621

Math Focus: Mainly analysis and algebra
$$\begin{align*}
S_n &= \phantom{-}u_1+u_1r+u_1r^2 + \ldots u_1r^{n-2} + u_1r^{n-1} \\
rS_n &= \phantom{-u_1+} u_1r+u_1r^2 + \ldots u_1r^{n-2} + u_1r^{n-1} + u_1 r^n \\
\text{and now subtract the aligned terms} \qquad rS_n-Sn &= -u_1 \phantom{+u_1r+u_1r^2 + \ldots u_1r^{n-2} + u_1r^{n-1}}+ u_1 r^n \\
&= u_1r^n - u_1
\end{align*}$$
Thanks from Tomedb
v8archie is offline  
October 26th, 2016, 11:58 AM   #3
Newbie
 
Joined: Oct 2016
From: UK

Posts: 7
Thanks: 0

Ah, so I tried to subtract vertically adjacent terms, rather than subtracting the sum of the terms.

Thank you very much for your help.
Tomedb is offline  
October 26th, 2016, 02:21 PM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,636
Thanks: 2621

Math Focus: Mainly analysis and algebra
Your approach can be seen to work if you put successive terms next to each other. You should see a telescoping series.
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
formula, geometric, proof, question, series



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Geometric Series Formula Monox D. I-Fly Algebra 5 October 11th, 2014 06:10 AM
Geometric series question Fozmass Applied Math 2 August 7th, 2014 05:23 AM
Geometric Series Question Help Math_slayer Algebra 5 May 11th, 2012 07:30 PM
derivation of integration formula from geometric series zg12 Calculus 1 March 6th, 2010 10:57 AM
Geometric Series Question Help Math_slayer Real Analysis 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.