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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^(n1) = 2^(n) 1 step 1: Prove n=1 2^11 = 1 step 2: assume true for n=k 1+2+2^2+....+2^(k1) = 2^(k) 1 step 3: Find next term n=k+1 1+2+2^2+....+2^(k1) + 2^((k+1)1) = 2^(k+1) 1 step 4: show true for n=k+1 1+2+2^2+....+2^(k1) = 2^(k) 1 1+2+2^2+....+2^(k1) + 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.


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