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    svenghart's Avatar
    svenghart Posts: 1, Reputation: 1
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    #1

    Dec 11, 2006, 03:09 PM
    Proof by induction
    I need help in figuring out how to prove 1+2n is less than or equal to 3^n by using induction.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Dec 11, 2006, 05:59 PM
    Prove by induction: 1+2n<=3^n

    #1. P_1 is true, since 1+2(1)<=3^1

    #2. Assume P_k is true, 1+2k<=3^k.

    Now, 1+2(k+1)<=3(1+2k) for k>=1--->2k+3<6k+3

    We can see that 3(1+2k)<=3*3^k

    3(1+2k)<=3^(k+1)

    And conclude that 1+2(k+1) <= 3^(k+1)
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