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 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. October 26th, 2016, 08:27 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 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 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. October 26th, 2016, 02:21 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 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. Tags formula, geometric, proof, question, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Monox D. I-Fly Algebra 5 October 11th, 2014 06:10 AM Fozmass Applied Math 2 August 7th, 2014 05:23 AM Math_slayer Algebra 5 May 11th, 2012 07:30 PM zg12 Calculus 1 March 6th, 2010 10:57 AM Math_slayer Real Analysis 0 December 31st, 1969 04:00 PM

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