How can i prove that $a_n \geq a_{n+1}$ for $n > 1$?
31174
Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
88838
How can I prove this inequality for $n\geq 2$?
71639
Proof $(1+1/n)^n$ is an increasing sequence
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
65168
Proof of sequence inequality
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
78144
How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$