November 22nd, 2010, 11:29 AM  #1 
Member Joined: Oct 2010 Posts: 30 Thanks: 0  proof recurrence
could someone show me how to prove this please The sequence u1,u2,u3,... is defined recursively by the rules that u1 =6,u2 =9, and for n ? 3, un = 3u n?1+18u n?2. Prove that un is a multiple of 3^n for all n ? N 
November 22nd, 2010, 11:42 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: proof recurrence
Notice that the coefficient of un1 is divisible by 3 and the coefficient of un2 is divisible by 3^2: .

November 22nd, 2010, 09:49 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: proof recurrence Hello, riotsandravess! Quote:
We can find the closed form for the sequence, but it takes a bit of work . . . [color=beige]. . [/color] [color=beige]. . [/color]  

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