推 assassin88:k!+3k <= k!+k*k (因為n>=4 且 n=k+1) < k!+k*k! 03/10 17:30
→ keepoo:因為k>n≧4 所以k*k>3*k 而k*k!>k*k這顯然吧 03/10 17:31
Prove by induction that n平方<n! for integer n>=4
直接跳到 考慮n=k+1:
(k+1)^2=k^2+2k+1<K!+2k+1<k!+2k+k=K!+3K<k!+kxk (這一步驟怎麼來的）
<k!+k(k!)(還有這一步驟） =(k+1)!
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