Algebra Pre-Algebra and Basic Algebra Math Forum

 April 8th, 2014, 04:01 AM #1 Senior Member   Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18 induction Use the method of induction to prove that the sum of first n odd numbers is equal to n^2 My attempt: for n = 1 1 = 1^2 = 1 So it is true for n = 1 Assume true for 1 + 3 + 5 +...+ 2n - 1 = n^2 Now try for (n + 1)th term 1 + 3 + 5 +...+ 2n - 1 + 2(n + 1) -1 = n^2 + 2(n + 1) - 1 = n^2 + 2n + 2 - 1 = n^2 + 2n + 1 = (n + 1)^2 So it is true for 1, n and n + 1 Therefore the sum of first n odd numbers = n^2 Is this the correct method? Am I missing something? thanks April 8th, 2014, 04:26 AM #2 Senior Member   Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra You have not missed anything, your proof is perfect.  April 8th, 2014, 04:27 AM #3 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 The proof is correct, but there is no reason to represent 2n + 1 as 2(n + 1) - 1. Simply 1 + 3 + 5 +...+ (2n - 1) + (2n + 1) = n^2 + 2n + 1 (by IH) = (n + 1)^2. Also, it's a good idea to indicate where exactly the induction hypothesis is used. Thanks from shunya Tags induction 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 Tommy_Gun Algebra 14 June 2nd, 2012 12:52 AM TheTree Algebra 1 May 28th, 2012 01:35 PM TheTree Algebra 1 May 28th, 2012 11:54 AM gaussrelatz Algebra 4 September 28th, 2011 09:55 PM OriaG Calculus 0 December 31st, 1969 04:00 PM

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