query: Prove $(n!) ^2 > n^n$ for all $n > 3$ using Induction
positive_passages.docid: 2554
positive_passages.text: Show that if $n>2$, then $(n!)^2>n^n$.
negative_passages.docid: 4077
negative_passages.text: Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
negative_passages.docid: 119436
negative_passages.text: Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
negative_passages.docid: 16812
negative_passages.text: Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
negative_passages.docid: 66358
negative_passages.text: Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
negative_passages.docid: 95000
negative_passages.text: Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
negative_passages.docid: 85941
negative_passages.text: Proof by induction that $n^3 - n$ is divisible by $6$
negative_passages.docid: 59280
negative_passages.text: Need help with Proof by Strong Induction question
negative_passages.docid: 88055
negative_passages.text: Use induction to prove the following: $1! + 2! + .... + n! \le (n + 1)!$
negative_passages.docid: 31535
negative_passages.text: Solving an inequality : $n \geq 3$ , $n^{n} \lt (n!)^{2}$.
negative_passages.docid: 86479
negative_passages.text: How to Prove with Mathematical Induction $3^n > n^2$
negative_passages.docid: 96332
negative_passages.text: Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
negative_passages.docid: 136274
negative_passages.text: $n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
negative_passages.docid: 2197
negative_passages.text: Induction principle for $n!<n^n$
negative_passages.docid: 145891
negative_passages.text: Prove that $n! > \sqrt{n^n}, n \geq 3$
negative_passages.docid: 70625
negative_passages.text: Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
negative_passages.docid: 78726
negative_passages.text: Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.