query: Prove that $4^n > n^4$by induction for $n\ge 5$
positive_passages.docid: 152577
positive_passages.text: Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
negative_passages.docid: 85731
negative_passages.text: Prove by induction that $n! > n^2$
negative_passages.docid: 121544
negative_passages.text: Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
negative_passages.docid: 125297
negative_passages.text: Induction to prove $2n + 3 < 2^n$
negative_passages.docid: 2197
negative_passages.text: Induction principle for $n!<n^n$
negative_passages.docid: 68480
negative_passages.text: Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
negative_passages.docid: 10604
negative_passages.text: Prove $3^n > n^2$ by induction
negative_passages.docid: 59280
negative_passages.text: Need help with Proof by Strong Induction question
negative_passages.docid: 45914
negative_passages.text: Proving that $n!≤((n+1)/2)^n$ by induction
negative_passages.docid: 71650
negative_passages.text: Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
negative_passages.docid: 62556
negative_passages.text: Prove $3|n(n+1)(n+2)$ by induction
negative_passages.docid: 11867
negative_passages.text: Prove by induction that $n < 2^n$ for all $n \ge 1$
negative_passages.docid: 120227
negative_passages.text: Proving $6^n - 1$ is always divisible by $5$ by induction
negative_passages.docid: 30783
negative_passages.text: Prove inequality $n<3^n$ using mathematical induction
negative_passages.docid: 39175
negative_passages.text: Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
negative_passages.docid: 115866
negative_passages.text: Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
negative_passages.docid: 19701
negative_passages.text: Prove $5\mid2^{4n}-1$ by induction