\(\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{9x10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}\)
\(=\frac{2}{5}\)
đặt A=1/2*3+1/3*4+1/4*5..............1/9*10
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}\)
\(=\frac{4}{10}=\frac{2}{5}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{9x10}=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}=1-\frac{1}{10}=\frac{9}{10}\)
\(\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{9x10}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{5}{10}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)
cái kia nhầm nhé
1/2.3 + 1/3.4 +.....+ 1/9.10
= 1/2 - 1/3 + 1/3 - 1/4 +......+ 1/9 - 1/10
= 1/2 - 1/10
=4/10 = 2/5