Cauchy-Schwarz Inequality
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- Cauchy Schwarz The Cauchy Schwarz Inequality is (a1b1+a2b2+⋯+anbn)2≤(a1+a2+⋯+an)(b1+b2+⋯+bn)(\sqrt{a_1b_1}+\sqrt{a_2b_2}+\dots+\sqrt{a_nb_n})^2\le(a_1+a_2+\dots+a_n)(b_1+b_2+\do…
By Cody Johnson, Zack Chroman
- Inequalities (Part 4) We're look at three useful inequalities in this part. Cauchy Schwarz Inequality For all real numbers x1,x2,...,xnx_1, x_2, ..., x_nx1,x2,...,xn and y1,y…
By Zi Song Yeoh
- Inequalities (Part 5) This part will consists of applications of Cauchy Schwarz, Holder's and Titu Lemma on some problems. Prove that for all positive real numbers a,b,ca, b, ca…
By Zi Song Yeoh
- Let aaa and bbb be positive real numbers with a+b=1a+b=1a+b=1. Prove that a2a+1+b2b+1≥13\dfrac{a^2}{a+1}+\dfrac{b^2}{b+1}\geq \dfrac{1}{3}a+1a2+b+1b2≥31 (Source: Hungary)
By Taimur Khalid