Ta có : \(A=10\left(\frac{1}{1.2}+\frac{5}{2.3}+...+\frac{89}{9.10}\right)\)
\(\Rightarrow10\left(\frac{1}{2}+\frac{5}{6}+...+\frac{89}{90}\right)\)
\(\Rightarrow10\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\right]\)
\(\Rightarrow10\left[9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\right)\right]\)
\(\Rightarrow10\left[9-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\right]\)
\(\Rightarrow10\left[9-\frac{9}{10}\right]\)
\(\Rightarrow10.\frac{81}{10}\)
\(\Rightarrow A=81\)
~\(Study\) \(well\)~
✰ᗪɾɑɕυɭɑ✰
A = 10.(1/1.2+5/2.3+...+89/9.10)
A/10 = 1/1.2+5/2.3+...+89/9.10
1.9 - A/10 = (1 - 1/1.2) + (1 - 5/2.3) +...+ (1 - 89/9.10)
9 - A/10 = 1/1.2 + 1/2.3 +....+ 1/9.10
9 - A/10 = 1 - 1/2 +1/2 -1/3 +...+ 1/9 -1 /10
9 - A/10 = 1 +0 +0+...... + 0 - 1/10
9 - A/10 = 1- 1/10
9 - A/10 = 9/10
A/10 = 9 - 9/10
A/10 = 81/10
A = (81/10) . 10
A = 81.
Vậy A = 81