query: Mathematical Induction proof for $(n!)^2 > n^n$
positive_passages.docid: 2554
positive_passages.text: Show that if $n>2$, then $(n!)^2>n^n$.
negative_passages.docid: 48333
negative_passages.text: Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
negative_passages.docid: 143968
negative_passages.text: Proving this inequality by mathematical induction
negative_passages.docid: 71918
negative_passages.text: Mathematical Induction
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 145891
negative_passages.text: Prove that $n! > \sqrt{n^n}, n \geq 3$
negative_passages.docid: 148330
negative_passages.text: Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
negative_passages.docid: 82774
negative_passages.text: Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
negative_passages.docid: 90789
negative_passages.text: Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
negative_passages.docid: 143357
negative_passages.text: Comparing $2^n$ to $n!$
negative_passages.docid: 11867
negative_passages.text: Prove by induction that $n < 2^n$ for all $n \ge 1$
negative_passages.docid: 30783
negative_passages.text: Prove inequality $n<3^n$ using mathematical induction
negative_passages.docid: 19129
negative_passages.text: mathematical induction proof of a square vs factorial
negative_passages.docid: 86479
negative_passages.text: How to Prove with Mathematical Induction $3^n > n^2$
negative_passages.docid: 105854
negative_passages.text: Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
negative_passages.docid: 70386
negative_passages.text: Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
negative_passages.docid: 125028
negative_passages.text: Prove the following equality using mathematical induction: