query: Prove by Induction : $n < 2^n$
positive_passages.docid: 73683
positive_passages.text: Proof by induction - Being stuck before being able to prove anything!
negative_passages.docid: 2197
negative_passages.text: Induction principle for $n!<n^n$
negative_passages.docid: 33082
negative_passages.text: Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
negative_passages.docid: 95000
negative_passages.text: Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
negative_passages.docid: 90835
negative_passages.text: Use induction to prove that $2^n \gt n^3$ for every integer $n \ge 10$.
negative_passages.docid: 55266
negative_passages.text: Prove that $(n+1)^{n-1}<n^n$
negative_passages.docid: 135807
negative_passages.text: I'm having trouble with a proof by induction
negative_passages.docid: 59280
negative_passages.text: Need help with Proof by Strong Induction question
negative_passages.docid: 10604
negative_passages.text: Prove $3^n > n^2$ by 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: 88144
negative_passages.text: Induction Proof $n! < n^n$
negative_passages.docid: 134000
negative_passages.text: Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
negative_passages.docid: 49299
negative_passages.text: Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
negative_passages.docid: 155897
negative_passages.text: Proof by induction - is this correct?
negative_passages.docid: 67527
negative_passages.text: Proof by Induction that $3^n ≥ 1+2^n$
negative_passages.docid: 39175
negative_passages.text: Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
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