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November 22nd, 2010, 12:29 PM   #1
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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
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November 22nd, 2010, 12:42 PM   #2
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Re: proof recurrence

Notice that the coefficient of un-1 is divisible by 3 and the coefficient of un-2 is divisible by 3^2: .
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November 22nd, 2010, 10:49 PM   #3
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Re: proof recurrence

Hello, riotsandravess!

Quote:
Could someone show me how to prove this please?




We can find the closed form for the sequence, but it takes a bit of work . . .










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