Ta có: \(A=\frac{1}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+......+\frac{5}{64.69}\right)\)
\(\Rightarrow A=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+......+\frac{1}{64}-\frac{1}{69}\right)\)
\(\Rightarrow A=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{69}\right)=\frac{1}{5}\times\frac{65}{276}\)
\(\Rightarrow A=\frac{13}{276}\)
Vậy \(A=\frac{13}{276}\)
\(A=\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{64.69}\)
\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)
\(5A=\frac{1}{4}-\frac{1}{69}\)
\(A=\frac{65}{276}:5\)
\(A=\frac{13}{276}\)
\(A=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)
\(A=\frac{9-4}{1}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)
\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+....+\frac{1}{64}-\frac{1}{64}-\frac{1}{69}\)
\(5A=\frac{1}{4}-\frac{1}{69}\)
\(5A=\frac{65}{276}\)
\(A=\frac{65}{276}\div5=\frac{13}{276}\)