Prove by induction $4^n > n^2$ for $n \geq 1$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
8609
Prove by induction that $n!>2^n$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
126889
Proof by induction: inequality $n! > n^3$ for $n > 5$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
62177
Prove that: $2^n < n!$ Using Induction
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
10604
Prove $3^n > n^2$ by induction
280
Prove by induction that $5^n - 1$ is divisible by $4$.
40692
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$