Question

1/20+1/30+1/42+1/56+...+1/990

Cảm ơn trước !!! hihi

Answer 1

\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{9900}\)

\(=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{99\cdot100}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{4}-\frac{1}{100}\)

\(=\frac{24}{100}=\frac{6}{25}\)

Answer 2

Đặt A=1/20+1/30+1/42+1/56+...+1/930

 =>A=1/4.5+1/5.6+1/6.7+...+1/30.31

=>A=1/4-1/5+1/5-1/6+...+1/30-1/31

=>A=1/4-1/31

=>A=31/124-4/124

=>A=27/124

Vây A=27/124

đề bài sai à bn phải là 1/930 chứ