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 July 16th, 2012, 02:21 PM #1 Member   Joined: Jun 2012 Posts: 76 Thanks: 0 mathematical induction question this is what i have 1+2+2^2+....+2^(n-1) = 2^(n) -1 step 1: Prove n=1 2^1-1 = 1 step 2: assume true for n=k 1+2+2^2+....+2^(k-1) = 2^(k) -1 step 3: Find next term n=k+1 1+2+2^2+....+2^(k-1) + 2^((k+1)-1) = 2^(k+1) -1 step 4: show true for n=k+1 1+2+2^2+....+2^(k-1) = 2^(k) -1 1+2+2^2+....+2^(k-1) + 2^((k+1)-1) = 2^(k) -1 + 2^((k+1)-1) = 2^k -1 +2^k = ? this is where i am stuck. i know the answer is 2^(k+1)-1 but i dont know how to get there from where i am. please help. July 16th, 2012, 02:39 PM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: mathematical induction question [color=#000000]You want to prove that . For n=1 you get 1=1 Suppose it holds for n=k, meaning that , you will have to prove that the equation holds for n=k+1. Indeed for n=k+1, .[/color] July 16th, 2012, 02:46 PM #3 Member   Joined: Jun 2012 Posts: 76 Thanks: 0 Re: mathematical induction question ahhh ok i didnt know that 2x2^k = 2^(k+1) that is where i was getting stuck. thanks! huge help July 16th, 2012, 03:20 PM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: mathematical induction question Recall the law of exponents: hence: July 16th, 2012, 07:47 PM #5 Member   Joined: Jun 2012 Posts: 76 Thanks: 0 Re: mathematical induction question ok im lost again. why is it 2x2^k and not 2^k+2^k July 16th, 2012, 07:57 PM #6 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: mathematical induction question Both are equivalent: July 17th, 2012, 10:56 AM #7 Member   Joined: Jun 2012 Posts: 76 Thanks: 0 Re: mathematical induction question ok i get it. i asked the teacher about it as well and she explained it some more. Tags induction, mathematical, question 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 alloy Algebra 1 December 18th, 2012 07:30 AM medos Algebra 5 October 31st, 2012 03:54 PM firstsin Algebra 7 January 28th, 2012 11:09 AM Sunde Algebra 14 August 3rd, 2011 04:10 PM tri4thlete Computer Science 4 March 29th, 2010 01:13 PM

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