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Math Help - recurison + induction

  1. #1
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    recurison + induction

    -1 for n greater/equal to 1

    Last edited by Tom123; November 7th 2007 at 07:36 AM.
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  2. #2
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    Prove by induction:

    f_{2}+f_{4}+.........+f_{2n}=f_{2n+1}-1

    Prove for n=1:

    f_{2(1)+1}-1=f_{3}-1=2-1=1......true.

    Assume P_{k} is true:

    f_{2}+f_{4}+...........+f_{2k}=f_{2k+1}-1

    now, we must show that P_{k+1} is true:

    f_{2}+f_{4}+...........+f_{2(k+1)}=f_{2(k+1)+1}-1 is true.

    f_{2}+f_{4}+...........+f_{2k}+f_{2k+2}=\underbrac  e{f_{2k+1}+f_{2k+2}}_{\text{this is f(2k+3)}}-1

    f_{2k+1}+f_{2k+2}=f_{2k+3} and the proof is complete.
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