N 2 n proof
,,Hint only: For n≥3 you have n2>2n+1 (this should not be hard to see) so if n2<2n then consider 2n+1=2⋅2n>2n2>n2+2n+1=(n+1)2. ,,,Suppose that when n=k (k≥4), we have that k!>2k. Now, we have to prove that (k+1)!>2k+1 when n=(k+1)(k≥4). (k+1)!=(k+1)k!>(k+1)2k (since k!>2k). ,n+1<n+n<2n+2n=2n+1. ,n+1<n+n<2n+2n=2n+1. ,
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 N 2 n proof 相關參考資料
#6 Proof prove by induction n less 2n n squared less 2 to the n ...
https://www.youtube.com Inequality Mathematical Induction Proof: 2^n greater than n^2
https://www.youtube.com Proof that $n^2 < 2^n$ - Mathematics Stack Exchange
Hint only: For n≥3 you have n2>2n+1 (this should not be hard to see) so if n2<2n then consider 2n+1=2⋅2n>2n2>n2+2n+1=(n+1)2. https://math.stackexchange.com Proof that 2^n is greater than n. - YouTube
https://www.youtube.com Prove 2^n is greater than n - YouTube
https://www.youtube.com Prove by induction that $n!>2^n$ - Mathematics Stack Exchange
Suppose that when n=k (k≥4), we have that k!>2k. Now, we have to prove that (k+1)!>2k+1 when n=(k+1)(k≥4). (k+1)!=(k+1)k!>(k+1)2k (since k!>2k). https://math.stackexchange.com Prove by mathematical induction: $n < 2^n
n+1<n+n<2n+2n=2n+1. https://math.stackexchange.com Prove by mathematical induction: n<2n [duplicate] - Math ...
n+1<n+n<2n+2n=2n+1. https://math.stackexchange.com Prove n! is greater than 2^n using Mathematical Induction ...
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