D= 3/3x4+3/4x5+...+3/99x100
D=3x(1/3x4+1/4x5+....+1/99x100)
D=3x(1/3-1/4+1/4-1/5+...+1/99-1/100)
D=3x(1/3-1/100)
D=3x(100/300-3/300)
D=3x97/300=97/100
Nhớ tk cho mình nha
\(D=\frac{3}{3\times4}+\frac{3}{4\times5}+...+\frac{3}{98\times99}+\frac{3}{99\times100}\)
\(=3\times\left(\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{98\times99}+\frac{1}{99\times100}\right)\)
\(=3\times\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=3\times\left(\frac{1}{3}-\frac{1}{100}\right)\)
\(=3\times\frac{97}{300}\)
\(=\frac{97}{100}\)