query: Show that $n>(\log n)^k$ for sufficiently large values of $n$
positive_passages.docid: 144719
positive_passages.text: How to find $\lim\limits_{n\rightarrow \infty}\frac{(\log n)^p}{n}$
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
negative_passages.docid: 71650
negative_passages.text: Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
negative_passages.docid: 88838
negative_passages.text: How can I prove this inequality for $n\geq 2$?
negative_passages.docid: 59535
negative_passages.text: Prove that there exists such a set of $n$ positive integers
negative_passages.docid: 148455
negative_passages.text: Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 79187
negative_passages.text: Can we find $c_n$ to make $X_nc_n \rightarrow 0$ almost surely, even if $EX_n > \infty$?
negative_passages.docid: 117761
negative_passages.text: When is $\binom{n}{k}$ divisible by $n$?
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.
negative_passages.docid: 88144
negative_passages.text: Induction Proof $n! < n^n$
negative_passages.docid: 75373
negative_passages.text: Show that $2^n>n$ for $n\in \mathbb{N}$
negative_passages.docid: 70067
negative_passages.text: Asymptotics of $\max\limits_{1\leqslant k\leqslant n}X_k/n$
negative_passages.docid: 149056
negative_passages.text: Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
negative_passages.docid: 144633
negative_passages.text: Verification of proof involving logarithms and limits
negative_passages.docid: 13330
negative_passages.text: Inductive Proof that $k!<k^k$, for $k\geq 2$.
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$