Question

A = 3/54 + 5/126 + 7/294 + 8/609

TÍNH BẰNG CÁCH THUẬN TIỆN NHẤT

Answer 1

\(A=\frac{3}{54}+\frac{5}{126}+\frac{7}{294}+\frac{8}{609}\)

\(\Rightarrow A=\frac{3}{9.6}+\frac{5}{2.7.9}+\frac{7}{7.7.6}+\frac{8}{3.7.29}\)

\(\Rightarrow A=\frac{1}{18}+\frac{5}{7.18}+\frac{1}{6.7}+\frac{8}{3.7.29}\)

\(\Rightarrow A=\frac{7+5}{7.18}+\frac{1}{6.7}+\frac{8}{3.7.29}\)

\(\Rightarrow A=\frac{2}{7.3}+\frac{1}{6.7}+\frac{8}{3.7.29}\)

\(\Rightarrow A=\frac{1}{3.7}\left(\frac{2}{1}+\frac{1}{2}+\frac{8}{29}\right)\)

\(\Rightarrow A=\frac{1}{21}\left(\frac{116+29+16}{58}\right)\)

\(\Rightarrow A=\frac{1}{21}.\frac{161}{58}\)

\(\Rightarrow A=\frac{161}{1218}=\frac{23}{174}\)

Vậy \(A=\frac{23}{174}\)