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August 12th, 2011, 10:00 AM  #1 
Newbie Joined: Aug 2011 Posts: 2 Thanks: 0  How to proof this is true by induction **STUCK**
Hi guys, first of all thanks for your help. I'm stuck with this problem, i need to proof the following: 5^(n+1) + 2 * 3^n + 1 is divisible by 8 for any n >= 0 It's true for n = 0 5 + 2 + 1 = 8 How to proof that it's true for n+1 ?? Thanks!! 
August 12th, 2011, 10:20 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs  Re: How to proof this is true by induction **STUCK**
I would set my induction hypothesis as: where Then compute: Now, we may write: where since the sum of two odd numbers is even, thus adding equivalent expressions to both sides of the induction hypothesis, we have: Since we have derived from this completes the proof by induction. 
August 12th, 2011, 10:52 AM  #3 
Newbie Joined: Aug 2011 Posts: 2 Thanks: 0  Re: How to proof this is true by induction **STUCK**
Thanks Mark!

August 12th, 2011, 10:57 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs  Re: How to proof this is true by induction **STUCK**
Glad to help, and welcome to the forum! 

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