Question

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{49.50}\)

Answer 1

\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{49.50}\)

\(\Rightarrow\frac{1}{2}A=\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{4}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{2}A=\frac{6}{25}\)

\(\Rightarrow A=\frac{6}{25}:\frac{1}{2}=\frac{12}{25}\)

Answer 2

2A=2/2.2.3+2/2.3.4+...+2/2.49.50

2A=1/2.3+1/3.4+...+1/49.50

2A=1/2-1/3+1/3-1/4+....+1/49-1/50

2A=1/2-1/50

2A=12/25

A=12/25:2

A=6/25

Mk` tính nhẩm nên chưa chắc đã đúg. Bạn tính lại xem đúg ko nha!

Chúc pn họk tốt!!!!

Answer 3

Sorry. Mk` bị nhầm. Phải làk nhân 1/2 cơ

Answer 4

2A=\(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) +.........+\(\frac{1}{49.50}\)

2A=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{49}-\frac{1}{50}\)

2A=\(\frac{1}{2}-\frac{1}{50}\)

2A=\(\frac{12}{25}\)

A=\(\frac{12}{25}:2=\frac{6}{25}\)

Answer 5

\(\frac{12}{25}\)

Answer 6

A=2.(\(\frac{1}{2.3}\) +\(\frac{1}{3.4}\) +\(\frac{1}{4.5}\) +....+\(\frac{1}{49.50}\) ) 

A=2.(\(\frac{1}{2}\) -\(\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}\)- \(\frac{1}{50}\) )

A=2.(\(\frac{1}{2}\) -\(\frac{1}{50}\))

A=\(\frac{24}{25}\)