April 9th, 2015, 09:18 AM  #1 
Senior Member Joined: May 2012 Posts: 203 Thanks: 5  induction
I am not sure what constitutes as a proof by induction for the problem such as: an+1= (an+6)/2 , n=1,2... a1=2 show that an <6 for all n 
April 9th, 2015, 10:09 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 Math Focus: Mainly analysis and algebra 
$a_1= 2 \lt 6$ Assume $a_n \lt 6$ Then $a_{n+1} = {a_n + 6 \over 2} \lt {6 + 6 \over 2} = 6$. 

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