Question

 so sánh tổng sau với 1 : 8-3/2*4+3/4*6+3/6*8+.....+3/98*100

Answer 1

\(8-\frac{3}{2\cdot4}+\frac{3}{4\cdot6}+...+\frac{3}{98\cdot10}\)

\(=8-\frac{3}{2}\left[\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+...+\frac{1}{98\cdot100}\right]\)

\(=8-\frac{3}{2}\left[\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right]\)

\(=8-\frac{3}{2}\left[\frac{1}{2}-\frac{1}{100}\right]=8-\frac{3}{2}\cdot\frac{49}{100}=8-\frac{147}{200}=\frac{1453}{200}>1\)