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    • Thread Starter

    Hi guys,

    I wonder if anybody could help me do an FP1 question on Induction ( q.10, p.105, ex.6)

    The question is:

    "Prove that if Un+2=3Un+1 -2Un for n being an element of the set of natural numbers, and if U1=1 , U2=3, then Un=(2^n)-1."

    Could someone please walk me through the steps of the solution? - I have no idea how to do a question with a Un+2 in. I know how to do it if there is an expression connecting Un+1 and Un

    Thanks a lot in advance!!
    • PS Helper

    PS Helper
    This is an induction question with 2 base cases. Usually you have one base case and you have to show that {true for k} implies {true for k+1}, whereas here you need to show that {true for k and k+1} implies {true for k+2}. So check that it holds true for the base cases (u_1 and u_2), and then check that if it's true for n=k,k+1 then it's true for n=k+2.

    That is, given that u_k=2^k-1 and u_{k+1}=2^{k+1}-1, show that u_{k+2}=2^{k+2}-1 using the formula.
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