Hints for showing that if $x,y \geq 0$, then $(x+y)^k \geq x^k + y^k$ for all $k \geq 1$
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
20467
Show that $(y_n)\in l^q$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
16524
Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$