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proving big Oso, I have a question that is stated: prove 2^n=O(n!) here is my attempt to prove that the statement is true or false: 2^1=2 1!=1 false 2 is not <= 1 2^2=4 2!=2 false 4 is not <=2 2^3=8 3!=6 false 8 is not <= 6 2^4=16 4!=24 true 16<=24 2^5=32 5!=120 it looks like the statement is true only when n is greater then or equal to 4. am I following this correctly? |

Re: proving big O"It looks like" isn't going to help here, since you're asked to prove the inclusion. Here's a thought. Suppose 2^n < n! for some n > 1. Then 2^(n+1) = 2^n * 2 < n! * 2 < n! * (n+1) = (n+1)!. |

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