3^n < n! for all n > 6 with n ∈ N.

mathematical induction to prove these?

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- Nov 26th 2008, 04:59 AMcaptainjapanProve by induction
3^n < n! for all n > 6 with n ∈ N.

mathematical induction to prove these? - Nov 26th 2008, 06:06 AMSoroban
Hello, captainjapan!

Quote:

Prove by induction: .

. . . . . True

Assume

Multiply both sides by 3: . .[1]

. . Since

. . Multiply by .[2]

Combine [1] and [2]: .

. . Therefore: .

And we have proved . . . The inductive proof is complete.