\(\frac{8}{9}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-...-\frac{1}{6}-\frac{1}{2}\)

\(\Rightarrow\frac{8}{9}-\left(\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+...+\frac{1}{6}+\frac{1}{2}\right)\)

\(\Rightarrow\frac{8}{9}-\left(\frac{1}{9.8}+\frac{1}{8.7}+\frac{1}{7.6}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(\Rightarrow\frac{8}{9}-\left(\frac{1}{9}-\frac{1}{8}+\frac{1}{8}-\frac{1}{7}+...+\frac{1}{2}-1\right)\)

\(\Rightarrow\frac{8}{9}-\left(1-\frac{1}{9}\right)\)

\(\Rightarrow0\)

Tìm Min à bạn?

\(Q=\left|x-2\right|+\left|x-5\right|+\left|x+1\right|\)

\(=\left|x-2\right|+\left|5-x\right|+\left|x+1\right|\)

\(=\left(\left|x-2\right|+\left|x-5\right|\right)+\left|x+1\right|\)

\(=\left(\left|2-x+5-x\right|\right)+\left|x+1\right|\)

\(=\left|3\right|+\left|x+1\right|=\left|3+x+1\right|=\left|x+4\right|\)

Mà \(\left|x+4\right|\ge0\forall x\Rightarrow MinQ=0\)

Dấu '' = '' xảy ra khi \(x+4=0\Leftrightarrow x=-4\)

\(P=\left|x+1\right|+\left|x+2\right|+\left|x+3\right|\)

\(=\left(\left|x+1+x+2\right|\right)+\left|x+3\right|\)

\(=\left(\left|2x+3\right|+\left|x+3\right|\right)\)

\(=\left|2x+3+x+3\right|\)

\(=\left|3x+6\right|\ge0\)

Dấu '' = '' xảy ra khi \(3x+6=0\Rightarrow3x=-6\Rightarrow x=-2\)

Đặt đại 1 cái tên kk

\(N=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{100.103}\)

\(\Rightarrow3N=3\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{100.103}\right)\)

\(\Rightarrow3N=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{100.103}\)

\(\Rightarrow3N=\frac{1}{1}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{103}\)

\(\Rightarrow3N=\frac{1}{1}-\frac{1}{103}\)

\(\Rightarrow N=\frac{102}{103}:3\)

\(\Rightarrow N=\frac{34}{103}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1999.2000}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1999}-\frac{1}{2000}\)

\(=1-\frac{1}{2000}\)

\(=\frac{1999}{2000}\)