Question:Prove by mathematical induction that if Un+2= 3Un+1 - 2Un for all positive integers n, and U1 = 1 , U2 = 3 , then Un = 2n - 1.
How to deal with relations that includes 3 terms in mathematical induction?
This is how far I got:
Un = 2n - 1
Assume when n=k, the equation is true: Uk = 2k -1
Proof that Uk+1=2k+1-1
UK+1= 3Uk -2Uk-1
=3( 2k - 1) -2Uk-1 Then I couldn't proceed with the k-1 there. Can anyone help?