Question

7/1.2+7/2.3+.....+7/10.11=?

ai giải đúng và nhanh thì mk sẽ tk cho

 

Answer 1

Đặt \(A=\frac{7}{1\cdot2}+\frac{7}{2\cdot3}+...+\frac{7}{10\cdot11}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{7}\left(\frac{7}{1\cdot2}+\frac{7}{2\cdot3}+...+\frac{7}{10\cdot11}\right)\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{10\cdot11}\)

\(\Rightarrow\frac{1}{7}A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\)

\(\Rightarrow\frac{1}{7}A=1-\frac{1}{11}\)

\(\Rightarrow\frac{1}{7}A=\frac{10}{11}\)

\(\Rightarrow A=\frac{10}{11}:\frac{1}{7}\)

\(\Rightarrow A=\frac{70}{11}\)