Question

1/2.5+1/5.8+.....+1/23.26+1/26.29

Gải giúp mình với, mình cảm ơn

Answer 1

Đặt A = \(\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{23.26}+\frac{1}{26.29}\)
     3A = \(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{23.26}+\frac{3}{26.29}\)
          = \(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}\)
          = \(\frac{1}{2}-\frac{1}{29}\)\(=\frac{27}{58}\)
     A = \(\frac{27}{58}:3=\frac{9}{58}\)
 

Answer 2

\(\frac{1}{2.5}+\frac{1}{5.8}+...+\frac{1}{23.26}+\frac{1}{26.29}=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{23.26}+\frac{3}{26.29}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}\right)=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{29}\right)\)

\(=\frac{1}{3}.\frac{27}{58}=\frac{9}{58}\)

Answer 3

Đặt A = \(\frac{1}{2.5}+\frac{1}{5.8}+.....+\frac{1}{23.26}+\frac{1}{26.29}\) 

\(\Rightarrow3A=\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{23.26}+\frac{3}{26.29}\)

\(\Rightarrow3A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}\)

\(\Rightarrow3A=\frac{1}{2}-\frac{1}{29}\) 

\(\Rightarrow3A=\frac{27}{58}\)

\(\Rightarrow A=\frac{27}{58}:3\)

\(\Rightarrow A=\frac{9}{58}\)