Question

Thực hiện phép tính:

\(A=\frac{1}{4\times9}+\frac{1}{9\times14}+....+\frac{1}{64\times69}\)

Trình bày rõ ràng nha các bạn.GGGGGGGGIIIIIUUUPPPP MMMMMMIIIINNNNHH! Ai nhanh nhất mik tick cho!

Answer 1

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 \(A=\frac{13}{276}\)

Answer 2

\(A=\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{64.69}\)

\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(5A=\frac{1}{4}-\frac{1}{69}\)

\(A=\frac{65}{276}:5\)

\(A=\frac{13}{276}\)

Answer 3

\(A=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)

\(A=\frac{9-4}{1}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)

\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+....+\frac{1}{64}-\frac{1}{64}-\frac{1}{69}\)

\(5A=\frac{1}{4}-\frac{1}{69}\)

\(5A=\frac{65}{276}\)

\(A=\frac{65}{276}\div5=\frac{13}{276}\)