Prove that: $\prod_{k=1}^n \sin^2(2^kx)\le (3/4)^{n-1}.$
120795
Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$
79685
For natural $n$, prove $\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}$
59905
Proving the inequality $\frac{n^k}{k^k}\leq\binom{n}{k}\leq\frac{n^k}{k!}$ involving binomial coefficient.
13864
$\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
21921
Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
136652
Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$
142992
Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
51679
Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.