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Math Help - mathematical induction

  1. #1
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    mathematical induction

    Prove that 3^n \geq 3n.
    If n=1, then 3^1=3(1). Clearly, this is true.
    Assume n=k and 3^k \geq 3k.
    If n=k+1, then 3^{k+1}=3^k 3
    I am stuck here. Can someone explain how to show 3^{k+1} \geq 3(k+1)? Thank you.
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  2. #2
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    Quote Originally Posted by dori1123 View Post
    Prove that 3^n \geq 3n.
    If n=1, then 3^1=3(1). Clearly, this is true.
    Assume n=k and 3^k \geq 3k.
    If n=k+1, then 3^{k+1}=3^k 3
    I am stuck here. Can someone explain how to show 3^{k+1} \geq 3(k+1)? Thank you.
    note that k \ge 1, so that

    3^{k + 1} = 3 \cdot 3^k \ge 3 \cdot 3k > 3k + 3k \ge 3k + 3 = 3(k + 1)
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