What is the non-inductive proof of this inequality?
88059
Elementary central binomial coefficient estimates
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
32427
Basic mathematical induction regarding inequalities
85210
Proof by induction of the Inequality of Harmonic numbers: $H_{2^n} \ge 1+ \frac n2$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
61939
Induction of inequality involving AP
116781
Could someone give a detailed (yet elementary) proof for Jensen's inequality?
125707
A simple proof (hopefully) for $2^x \neq 0$
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
80556
Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
25775
How to prove $(1+1/x)^x$ is increasing when $x>0$?
144500
Cauchy-Schwarz inequality proof (but not the usual one)
33637
Proofs of the Cauchy-Schwarz Inequality?