Proving the inequality $2^n ≤2^{n+1}−2^{n−1}−1$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
85210
Proof by induction of the Inequality of Harmonic numbers: $H_{2^n} \ge 1+ \frac n2$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
145274
Prove by induction $\sum \frac {1}{2^n} < 1$
110153
How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
88838
How can I prove this inequality for $n\geq 2$?
67527
Proof by Induction that $3^n ≥ 1+2^n$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
156669
Trying to prove a simple (?) inequality