query: By induction, show that for ∀n∈N, it is true that:
positive_passages.docid: 15631
positive_passages.text: Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
negative_passages.docid: 135509
negative_passages.text: Proof writing: how to write a clear induction proof?
negative_passages.docid: 104349
negative_passages.text: Proof by induction involving symmetric groups
negative_passages.docid: 98372
negative_passages.text: Proof of the principle of backwards induction
negative_passages.docid: 121107
negative_passages.text: Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
negative_passages.docid: 12857
negative_passages.text: Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$
negative_passages.docid: 10424
negative_passages.text: Review of a proof for De Moivre's theorem using mathematical induction
negative_passages.docid: 126889
negative_passages.text: Proof by induction: inequality $n! > n^3$ for $n > 5$
negative_passages.docid: 52113
negative_passages.text: Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
negative_passages.docid: 19326
negative_passages.text: What makes induction a valid proof technique?
negative_passages.docid: 49299
negative_passages.text: Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
negative_passages.docid: 95000
negative_passages.text: Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
negative_passages.docid: 14435
negative_passages.text: Show by induction: $(1+\frac{1}{n})^{n}<n$
negative_passages.docid: 115866
negative_passages.text: Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
negative_passages.docid: 150819
negative_passages.text: How to prove by induction that $|\sin(nx)| \leq n|\sin x|$?
negative_passages.docid: 115435
negative_passages.text: Induction: prove using congruences
negative_passages.docid: 91197
negative_passages.text: Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction