How do I prove the inequality $H_{2^m}>1+\frac{m}{2}$?
131771
Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$
3030
Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
15237
Prove an inequality using complex analysis
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
101792
By expanding $e^x$ into a series prove the following inequality
91871
Proving quadratic inequalities?
156669
Trying to prove a simple (?) inequality
146885
How prove this inequality $\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+e}+\frac{d-e}{e+a}+\frac{e-a}{a+b}\ge 0$
151154
Prove the inequality $\sqrt\frac{a}{a+8} + \sqrt\frac{b}{b+8} +\sqrt\frac{c}{c+8} \geq 1$ with the constraint $abc=1$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
26962
Proving an inequality involving the logarithm function: $\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
90902
Prove $\frac{a+b+c}{abc} \leq \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}$.