Question

1 - 1/6 - 1/10 - 1/15 -...- 1/45

Answer 1

 

Đặt Biểu thức là A

\(\frac{A}{2}=\frac{1}{2}-\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\right)\)

\(\left(\frac{A}{2}\right)=\frac{1}{2}-\left(\frac{4-3}{3x4}+\frac{5-4}{4x5}+\frac{6-5}{5x6}+...+\frac{10-9}{9x10}\right)\)

\(\frac{A}{2}=\frac{1}{2}-\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(\frac{A}{2}=\frac{1}{2}-\left(\frac{1}{3}-\frac{1}{10}\right)=\frac{4}{15}\Rightarrow A=\frac{8}{15}\)