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Math Help - Mathematical Induction

  1. #1
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    Mathematical Induction

    Hello!
    I've got another problem about matematical induction.

    Any comments would be appreciated!

    Thanks!
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  2. #2
    Eater of Worlds
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    I reckon it's safe to assume n can be negative?.

    This may be kind of flimsy, but............

    Let n=0, then 5(0)+7(0)=0, true for n=0

    Let n=1, then 1=5(3)+7(-2), true for n=1.

    Let n=2, then 2=5(6)+7(-4), true for n=2.

    Let n=3, then 3=5(9)+7(-6), true for n=3.

    Let n=4, then 4=5(12)+7(-8), true for n=4.

    See the pattern?.

    So, we increase a by 3 and decrease b by 2

    n+1=5(k+3)+7(p-2)=5k+15+7p-14=5k+7p+1

    But 5k+7p = n. So the induction holds.
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