a0 = 2, a1 = 3 for any k ≥ 2 (k is a whole number) ak = 3ak-1 - 2ak-2 Prove: an = 2^(n) + 1
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Originally Posted by MATNTRNG a0 = 2, a1 = 3 for any k ≥ 2 (k is a whole number) ak = 3ak-1 - 2ak-2 Prove: an = 2^(n) + 1 Let's use a stronger form of induction here. Base case: , Yielding case: Assume and . By our use of induction, we're done.
Last edited by chiph588@; March 28th 2010 at 04:09 PM.
Originally Posted by MATNTRNG a0 = 2, a1 = 3 for any k ≥ 2 (k is a whole number) ak = 3ak-1 - 2ak-2 Prove: an = 2^(n) + 1 It is true for . Assume truth for all indexes up to and show now for : Tonio
Good one!
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