I want to prove The Cauchy-Schwarz inequality $\left(\sum_{i=1}^n x_iy_{i}\right)^2 \le \sum_{i=1}^n x_i^2 \sum_{i=1}^n y_{i}^2$
33637
Proofs of the Cauchy-Schwarz Inequality?
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
104807
Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$
95030
Proving the Cauchy-Schwarz inequality by induction
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
121548
proof of an inequality $ \left( 1+ \frac{x}{p} \right) ^{p}$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
29198
How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
156513
Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$
47644
Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
18399
Prove this inequality $\sum \cos{A}\ge\frac{1}{4}(3+\sum\cos{(A-B)})$