6A=2.4.6+4.6.(8-2)+.........+50.52.(54-48)

6A=2.4.6+4.6.8-2.4.6+............+50.52.54-48.50.52

6A=50.52.54

A=50.52.54:6

A=23400

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+................+\dfrac{2}{50.52}\)

\(=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+..............+\dfrac{1}{50}-\dfrac{1}{52}\)

\(=\dfrac{1}{2}-\dfrac{1}{52}=\dfrac{25}{52}\)

\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+.....+\dfrac{2}{50.52}\)

\(=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+.....+\dfrac{1}{50}-\dfrac{1}{52}\)

\(=\dfrac{1}{2}-\dfrac{1}{52}=\dfrac{25}{52}\)

tự làm đi thớt bài này quá dễ rồi

\(=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{50}-\dfrac{1}{52}=\dfrac{1}{2}-\dfrac{1}{52}=\dfrac{25}{52}\)

Ta có: \(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+...+\frac{1}{48\cdot50}\)

\(\Rightarrow2\cdot A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{48\cdot50}\)

\(\Rightarrow2\cdot A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{48}-\frac{1}{50}\)

\(\Rightarrow2\cdot A=\frac{1}{2}-\frac{1}{50}=\frac{12}{25}\)

\(\Rightarrow2\cdot A=\frac{12}{25}\)

hay \(A=\frac{12}{25}:2=\frac{12}{25}\cdot\frac{1}{2}=\frac{12}{50}=\frac{6}{25}\)

gọi tổng của 1+2+3+4+...+79 là M

                     2+3+4+...+80 là N

ta có A = M.N

từ 1 đến 79 hay từ 2 đến 80 có  (79-1) chia 1 + 1=79

M = (79+1).79 chia 2= 3160

N = (80+2).79chia 2= 3239

A = 3160 .3239 = 10235240