Đặt phép tính là A

Ta có :\(A=10.\left(\frac{1}{1.2}+\frac{5}{2.3}+...+\frac{89}{9.10}\right)\)

\(\Rightarrow A=10.\left(\frac{1}{2}+\frac{5}{6}+...+\frac{89}{90}\right)\)

\(\Rightarrow A=10.\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\right]\)

\(\Rightarrow A=10.\left[9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\right)\right]\)

\(\Rightarrow A=10.\left[9-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\right]\)

\(\Rightarrow A=10.\left[9-\left(1-\frac{1}{10}\right)\right]\)

\(\Rightarrow A=10.\left[9-\frac{9}{10}\right]\)

\(\Rightarrow A=10.\frac{81}{10}\)

\(\Rightarrow A=81\)

~ Hok tốt ~

giúp mk mk tích cho

A=10(1/1.2+5/2.3+...+89/9.10)

A=10(1/2+5/6+...+89/90)

A=10[(1-1/2)+(1-1/6)+.....+(1-1/90)

A=10(1-1/2+1-1/6+...+1-1/90)

A=10[(1+1+...+1)-(1/2+1/6+...+1/90)

           9 chữ số 1

A=10[9-(1/1.2+1/2.3+...+1/9.10)]

A=10[9-(1-1/2+1/2-1/3+...+1/9-1/10)]

A=10[9-(1-1/10)]

A=10(9-9/10)

A=90-9=81

sai đề

Ta có :\(A=10\left(\frac{1}{1.2}+\frac{5}{2.3}+...+\frac{89}{9.10}\right)\)

\(\Rightarrow10\left(\frac{1}{2}+\frac{5}{6}+...+\frac{89}{90}\right)\)

\(\Rightarrow10\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\right]\)

\(\Rightarrow10\left[9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\right)\right]\)

\(\Rightarrow10\left[9-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\right]\)

\(\Rightarrow10\left[9-\left(1-\frac{1}{10}\right)\right]\)

\(\Rightarrow\)\(10\left[9-\frac{9}{10}\right]\)

\(\Rightarrow10.\frac{81}{10}\)

\(\Rightarrow A=81\)

Làm rờ đó sai thì thôi nha.