Prove that: $(x_1+...+x_k)^2\leq 2(x_1^2+...+x_k^2)$.
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
88838
How can I prove this inequality for $n\geq 2$?
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
88328
Proof of $1+x\leq e^x$ for all x?
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
29679
Prove: $|x-y|\leq |x|+|y|$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
25458
Prove inequalities $2\sqrt{n+1}-2 \leq 1 + 1/\sqrt{2} + 1/\sqrt{3} + .... + 1/\sqrt{n}\leq 2\sqrt{n}-1$