Prove by induction that $b_n-a_n < (\frac {1}2)^n(b-a)$
17289
prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
138036
Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$
112907
Math Induction Proof: $(1+\frac1n)^n < n$
106502
Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
108596
Proof by induction for "sum-of"
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $